[{"data":1,"prerenderedAt":188},["ShallowReactive",2],{"page:\u002Ffa\u002Fcats\u002Fnotes":3,"mdc--ry5nzn-key":11,"logs-archives-\u002Ffa\u002Fcats\u002Fnotes-notes":22},{"title":4,"thumbnail":5,"description":6,"path":7,"body":8,"tocData":9,"type":10},"یادداشت","\u002Fcontent\u002Fblogging.webp","یادداشت ها","\u002Ffa\u002Fcats\u002Fnotes","\u003CLogsArchives cat='notes' \u002F>",[],"page",{"data":12,"body":13},{},{"type":14,"children":15},"root",[16],{"type":17,"tag":18,"props":19,"children":21},"element","logs-archives",{"cat":20},"notes",[],[23,65],{"title":24,"thumbnail":25,"description":26,"date":27,"cat":20,"intro":28,"comments":29,"newsletter":29,"toc":29,"path":30,"body":31,"tocData":32,"type":10},"اولین برخورد با پادماده","\u002Fcontent\u002Fpositrondiscovery.webp","فیزیک ذرات پر از شگفتی‌هایی است که درک ما از جهان را دگرگون کرده‌اند. یکی از این شگفتی‌ها پوزیترون است، پادذره‌ای که همزاد الکترون اما با بار مثبت است. کشف این ذره در سال 1932 نه‌تنها دریچه‌ای به دنیای پادماده گشود، بلکه به ما نشان داد که انرژی و ماده چگونه در هم تنیده‌اند. این یادداشت شما را به سفری در دنیای پوزیترون می‌بره: از لحظه کشفش تا کاربردهای امروزی‌اش. بیایید این ذره شگفت‌انگیز رو کشف کنیم و ببینیم چرا هنوز هم دانشمندان رو مجذوب خودش می‌کنه.","2023-02-05T12:29:12.649Z",false,true,"\u002Ffa\u002Flogs\u002Fthe-positron","## پوزیترون: پادذره‌ای که جهان را روشن کرد\n\nفیزیک ذرات پر از شگفتی‌هایی است که درک ما از جهان را دگرگون کرده‌اند. یکی از این شگفتی‌ها **پوزیترون** است، پادذره‌ای که همزاد الکترون اما با بار مثبت است. کشف این ذره در سال 1932 نه‌تنها دریچه‌ای به دنیای پادماده گشود، بلکه به ما نشان داد که انرژی و ماده چگونه در هم تنیده‌اند. این یادداشت شما را به سفری در دنیای پوزیترون می‌بره: از لحظه کشفش تا کاربردهای امروزی‌اش. بیایید این ذره شگفت‌انگیز رو کشف کنیم و ببینیم چرا هنوز هم دانشمندان رو مجذوب خودش می‌کنه.\n\n## کشف پوزیترون: لحظه‌ای تاریخی\n\nدر سال 1932، کارل اندرسون، فیزیک‌دان آمریکایی، در آزمایش‌هایش با **اتاقک ابر ویلسون** شواهدی از ذره‌ای عجیب پیدا کرد. این ذره، که بعدها **پوزیترون** نام گرفت، جرمی برابر با الکترون داشت اما بار الکتریکی مثبتش باعث می‌شد در میدان مغناطیسی به جهت مخالف خمیده بشه. این کشف، که جایزه نوبل فیزیک 1936 رو برای اندرسون به ارمغان آورد، اولین تأیید تجربی وجود پادماده بود و پیش‌بینی‌های نظری پل دیراک در مکانیک کوانتوم رو به واقعیت تبدیل کرد.\n\nمثال عملی: تصور کنید پرتوهای کیهانی رو ردیابی می‌کنید. رد پوزیترون در اتاقک ابر مثل یه امضای منحصربه‌فرد بود که نشون می‌داد چیزی فراتر از الکترون‌های معمولی وجود داره.\n\n## ویژگی‌ها و تولید پوزیترون\n\nپوزیترون ذره‌ای بنیادی با جرم تقریبی 9.11×10⁻³¹ کیلوگرم (مشابه الکترون) و بار الکتریکی +1.6×10⁻¹⁹ کولن است. این ذره به روش‌های مختلفی تولید می‌شه:\n\n- **پرتوزایی بتا مثبت**: در هسته‌های ناپایدار، پروتون به نوترون تبدیل می‌شه و پوزیترون آزاد می‌کنه (مثل در ایزوتوپ کربن-11).\n- **تولید جفت**: وقتی پرتوهای گاما با انرژی بالا (بیش از 1.022 MeV) به هسته اتم برخورد می‌کنن، جفت الکترون-پوزیترون تشکیل می‌شه.\n- **شتاب‌دهنده‌های ذرات**: در آزمایشگاه‌هایی مثل CERN، پوزیترون‌ها برای مطالعه ذرات تولید می‌شن.\n\nمثال عملی: تو یه آزمایشگاه، پرتو گاما به یه صفحه سربی تابیده می‌شه و ناگهان الکترون و پوزیترون ظاهر می‌شن، انگار انرژی به ماده زنده شده!\n\n## واکنش‌های پوزیترونی: رقص ماده و پادماده\n\nیکی از ویژگی‌های خیره‌کننده پوزیترون، رفتارش در برخورد با الکترونه. وقتی پوزیترون و الکترون به هم می‌رسن، طی فرایندی به نام **نابودی الکترون-پوزیترون**، هر دو ذره از بین می‌رن و جرمشون به انرژی خالص تبدیل می‌شه. نتیجه؟ دو فوتون گاما با انرژی 511 keV که در جهت‌های مخالف منتشر می‌شن. این فرایند، که دقیقاً با معادله انیشتین **E=mc²** توضیح داده می‌شه، یکی از زیباترین نمایش‌های تبدیل ماده به انرژیه.\n\nمثال عملی: تو دستگاه‌های PET اسکن پزشکی، نابودی پوزیترون-الکترون فوتون‌هایی تولید می‌کنه که برای تصویربرداری از بدن استفاده می‌شن.\n\n## ناپایداری پوزیترون: چرا کمیاب است؟\n\nپوزیترون روی زمین به‌صورت طبیعی پایدار نیست. به محض اینکه با یه الکترون برخورد کنه (که تو محیط ما فراوانه)، نابود می‌شه و به تابش الکترومغناطیسی تبدیل می‌شه. به همین دلیل، پادماده مثل پوزیترون تو دنیای روزمره ما کمیابه و فقط تو فرایندهای خاص (مثل پرتوزایی یا انفجارهای کیهانی) دیده می‌شه. این ناپایداری نشون می‌ده چرا جهان ما بیشتر از ماده ساخته شده و پادماده نقش کوچیکی توش داره.\n\n## کاربردهای عملی پوزیترون\n\nپوزیترون فقط یه کنجکاوی علمی نیست؛ کاربردهای واقعی و مهمی داره:\n\n- **پزشکی**: تو **توموگرافی گسیل پوزیترون (PET)**، پوزیترون‌ها برای تشخیص سرطان و بیماری‌های مغزی استفاده می‌شن.\n- **کیهان‌شناسی**: مطالعه پوزیترون‌های کیهانی (مثل اونایی که تلسکوپ Fermi رصد می‌کنه) به درک ماده تاریک و انفجارهای ابرنواختری کمک می‌کنه.\n- **فیزیک بنیادی**: آزمایش‌هایی مثل ALPHA در CERN از پوزیترون برای مطالعه پادماده و تقارن ماده-پادماده استفاده می‌کنن.\n\nمثال عملی: تو بیمارستان، PET اسکن با ردیابی فوتون‌های ناشی از نابودی پوزیترون، تومورها رو با دقت پیدا می‌کنه و جان آدما رو نجات می‌ده.\n\n## منابع و مطالعه بیشتر\n\nبرای اطلاعات بیشتر، این منابع رو پیشنهاد می‌کنم:\n\n- **ویکی‌پدیا**: [پوزیترون](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPositron) (برای جزئیات پایه)\n- **CERN**: مقالات درباره پادماده و آزمایش‌های پوزیترون\n- **Scientific American**: مطالب عمومی درباره پادماده\n\nانجمن‌های آنلاین مثل Physics Stack Exchange هم برای بحث و پرس‌وجو عالی‌ان.\n\n## جمع‌بندی\n\nکشف پوزیترون نقطه عطفی تو تاریخ فیزیک بود که نه‌تنها وجود پادماده رو ثابت کرد، بلکه راه رو برای پیشرفت‌هایی تو پزشکی، کیهان‌شناسی و فیزیک بنیادی باز کرد. از لحظه‌ای که رد این ذره تو اتاقک ابر دیده شد تا کاربردهای امروزی‌اش تو PET اسکن، پوزیترون داستانی از شگفتی و علم رو روایت می‌کنه. آماده‌اید که بیشتر درباره اسرار کیهان کشف کنید؟ بیایید دست به کار بشیم و دنیای ذرات رو کاوش کنیم!",[33,37,41,45,49,53,57,61],{"title":34,"url":35,"items":36},"پوزیترون: پادذره‌ای که جهان را روشن کرد","#پوزیترون-پادذرهای-که-جهان-را-روشن-کرد",[],{"title":38,"url":39,"items":40},"کشف پوزیترون: لحظه‌ای تاریخی","#کشف-پوزیترون-لحظهای-تاریخی",[],{"title":42,"url":43,"items":44},"ویژگی‌ها و تولید پوزیترون","#ویژگیها-و-تولید-پوزیترون",[],{"title":46,"url":47,"items":48},"واکنش‌های پوزیترونی: رقص ماده و پادماده","#واکنشهای-پوزیترونی-رقص-ماده-و-پادماده",[],{"title":50,"url":51,"items":52},"ناپایداری پوزیترون: چرا کمیاب است؟","#ناپایداری-پوزیترون-چرا-کمیاب-است",[],{"title":54,"url":55,"items":56},"کاربردهای عملی پوزیترون","#کاربردهای-عملی-پوزیترون",[],{"title":58,"url":59,"items":60},"منابع و مطالعه بیشتر","#منابع-و-مطالعه-بیشتر",[],{"title":62,"url":63,"items":64},"جمع‌بندی","#جمعبندی",[],{"title":66,"thumbnail":67,"description":68,"date":69,"cat":20,"intro":28,"comments":29,"newsletter":29,"toc":29,"path":70,"body":71,"tocData":72,"type":10},"مقاله ای در مورد خود یادگیری فیزیک نوین","\u002Fcontent\u002Fphysics.webp","فیزیک؛ یکی از قدیمی‌ترین و پایه‌ای‌ترین علوم طبیعی است و شاید قدیمی‌ترین مبحث آن را بتوان اخترشناسی نامید. مدارکی وجود دارد که نشان می‌دهد هزاران سال پیش از میلاد مسیح، اقوامی همچون سومری‌ها و همچنین اقوامی در مصر باستان و اطراف سند تحقیقات و درک پیشگویانه‌ای (گمانه‌زنی‌هایی) از حرکت خورشید، ماه و ستارگان داشته‌اند.(ویکی‌پدیا)","2023-01-16T16:07:56.966Z","\u002Ffa\u002Flogs\u002Fself-learning-physics","## پیشگفتار\n\nفیزیک، علمی که جهان را توضیح می‌دهد، نه‌تنها دانشی عمیق و دقیق است، بلکه داستانی از کنجکاوی انسان برای درک رازهای هستی است. از سیاه‌چاله‌های مرموز تا رقص ذرات کوانتومی، فیزیک با زیبایی و ظرافتش ما را به شگفتی وا می‌دارد. اما پیچیدگی‌های ریاضی و سیستم‌های دانشگاهی گاهی لذت این علم را تحت‌الشعاع قرار می‌دهند. خوشبختانه، منابعی وجود دارند که یادگیری فیزیک را برای همه ممکن می‌کنند. این مقاله، با الهام از یادداشت سوزان ریگتی، دوره‌های خودآموز فیزیک را معرفی می‌کند که از مفاهیم پایه تا موضوعات پیشرفته را پوشش می‌دهند. بیایید سفری به دنیای فیزیک داشته باشیم و راهی برای کشف این علم پیدا کنیم.\n\n## فیزیک چیست؟ کلیدی برای درک جهان\n\nفیزیک مطالعه طبیعت و قوانین حاکم بر آن است، از حرکت سیارات در کهکشان‌ها تا رفتار ذرات زیراتمی. این علم، ستون تمدن مدرن است: از فناوری‌های پزشکی مثل MRI تا اینترنت و GPS، همگی ریشه در اکتشافات فیزیک دارند. موضوعات جذاب فیزیک شامل:\n\n## مکانیک کلاسیک: حرکت اجسام، از پرتاب یک توپ تا مدار ماه.\n\nنسبیت: توضیح زمان و فضا، مثل خمیدگی نور در نزدیکی سیاه‌چاله‌ها.\nکوانتوم: دنیای عجیب ذرات، که پایه کامپیوترهای کوانتومی است.\nماده تاریک و انرژی تاریک: رازهایی که 95% کیهان را تشکیل می‌دهند.\nمثال عملی: وقتی با GPS مسیر پیدا می‌کنید، نسبیت عام اینشتین زمان‌بندی سیگنال‌های ماهواره‌ای رو تنظیم می‌کنه تا دقیق باشه. فیزیک اینجاست، در زندگی روزمره ما.\n\n## چالش‌های یادگیری فیزیک\n\nفیزیک، با تمام زیبایی‌اش، پیچیدگی‌هایی داره. ریاضیات، زبان اصلی فیزیک، گاهی مفاهیم رو برای تازه‌کارها سنگین می‌کنه. توی سیستم‌های دانشگاهی، حجم فرمول‌ها و امتحانات می‌تونه لذت کشف رو کم‌رنگ کنه. حتی دانشجوهای فیزیک هم ممکنه به خاطر درگیری با مسائل ریاضی، حس کنجکاوی اولیه‌شون رو از دست بدن. سوزان ریگتی، فیزیک‌دان و نویسنده، توی مقاله‌اش اشاره می‌کنه که خیلی‌ها به فیزیک علاقه دارن، اما به دلایل مختلف (مثل نبود وقت یا دسترسی به منابع) نمی‌تونن دنبالش کنن. اینجاست که دوره‌های خودآموز وارد می‌شن.\n\n## معرفی دوره‌های سوزان ریگتی\n\nسوزان ریگتی، که خودش از فیزیک‌دان‌های برجسته و بنیان‌گذار شرکت‌های فناوری کوانتومیه، لیستی از دوره‌های خودآموز فیزیک رو پیشنهاد داده که برای علاقه‌مندان طراحی شده. این دوره‌ها، که از منابع باز مثل MIT OpenCourseWare، Khan Academy و کتاب‌های کلاسیک جمع‌آوری شدن، مسیری ساختاریافته برای یادگیری فیزیک ارائه می‌دن. از مکانیک پایه تا نسبیت عام و مکانیک کوانتوم، این دوره‌ها به شما کمک می‌کنن بدون نیاز به کلاس رسمی، فیزیک رو عمیق یاد بگیرین.\n\nلینک اصلی :‌\n\n[So You Want to Learn Physics…](https:\u002F\u002Fwww.susanrigetti.com\u002Fphysics)\n\n\u003Cdiv class=\"ltr\">\n\n## Before You Begin\n\n### **Popular library on Physics**\n\nWhen you're solving problems, working through textibrary, and getting into the nitty-gritty details of each topic, it's so easy to lose the forest for the trees and forget why you even became inspired to study physics in the first place. This is where really, really good (and non-speculative) popular library on physics come in handy: they inspire, they encourage, and they help you keep the big picture in mind.\n\nOne big problem is that many popular physics library (especially those written by famous physicists) are incredibly speculative and tend to present an unrealistic view of what the study of physics is all about. When you're learning physics, it's best to avoid these types of speculative library and stick to the ones that talk about the real physics that we know exists (in general, anything by [Frank Close](https:\u002F\u002Fwww.amazon.com\u002FFrank-Close\u002Fe\u002FB0032LWBQU?language=en_US&linkCode=ll2&linkId=3c7c04c8d21e464a287401f980430fd4&ref_=as_li_ss_tl&tag=susanfowler-20) or [Richard Feynman](https:\u002F\u002Fwww.amazon.com\u002FRichard-P.-Feynman\u002Fe\u002FB000AQ47U8?language=en_US&linkCode=ll2&linkId=ed2f3d4424a1dedaff83313cfbcd4668&ref_=as_li_ss_tl&tag=susanfowler-20) is a safe bet!).\n\nHere are a handful of my favorite popular physics library, ranked in order of difficulty:\n\n- [The First Three Minutes by Steven Weinberg](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0465024378\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0465024378&linkCode=as2&tag=susanfowler-20&linkId=d72aaa7813d719344a4c88258a5488d0) **(Level: Easy)**.An account of the Big Bang by one of the most brilliant physicists of all time.\n- [The Character of Physical Law by Richard Feynman](https:\u002F\u002Fwww.amazon.com\u002FCharacter-Physical-Law-MIT-Press\u002Fdp\u002F0262533413?dchild=1&keywords=character%20of%20physical%20law&language=en_US&linkCode=ll1&linkId=85b0a8234adfc1bb7a7c4b643f59bf6b&qid=1618957764&ref_=as_li_ss_tl&s=library&sr=1-1&tag=susanfowler-20) **(Level: Easy)**. A brilliant, inspiring little book on the laws of nature.\n- [The Particle Odyssey by Frank Close](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0198504861\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0198504861&linkCode=as2&tag=susanfowler-20&linkId=bfce048e1031401ef7c664d79ab2d927) **(Level: Easy)**. A brilliant popular introduction to particle physics and its history, beautifully illustrated with amazing figures and photographs. (Unfortunately it’s a bit difficult to find online right now, but if you find a copy, you should buy it ASAP!)\n- [Black Holes and Time Warps by Kip Thorne](https:\u002F\u002Fwww.amazon.com\u002FBlack-Holes-Time-Warps-Commonwealth\u002Fdp\u002F0393312763?dchild=1&keywords=black%20holes%20and%20time%20warps&language=en_US&linkCode=ll1&linkId=5c79d14a1bc80bbd2207736f7540668f&qid=1618958068&ref_=as_li_ss_tl&s=library&sr=1-1&tag=susanfowler-20) **(Level: Easy\u002FMedium)**. My absolute favorite popular introduction to general relativity.\n- [The Theoretical Minimum by Leonard Susskind and George Hrabovsky](https:\u002F\u002Fwww.amazon.com\u002FTheoretical-Minimum-Start-Doing-Physics\u002Fdp\u002F0465075681?dchild=1&keywords=the%20theoretical%20minimum&language=en_US&linkCode=ll1&linkId=e69e149c7cda69c3a460847a5e1b341c&qid=1618956738&ref_=as_li_ss_tl&sr=8-1&tag=susanfowler-20) **(Level: Medium)**. A solid introduction to classical mechanics. Is best understood around level 5 in the undergraduate curriculum.\n- [The Feynman Lectures on Physics (Boxed Set)](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0465023827\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0465023827&linkCode=as2&tag=susanfowler-20&linkId=47c82e27eae89efef1db2659759c65f7) and [Feynman Lectures on Physics (Kindle Edition)](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB016OMK7XW\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B016OMK7XW&linkCode=as2&tag=susanfowler-20&linkId=50edb7c48df214e8eb9a3a5e4d868806) **(Level: Medium)**. Feynman's Lectures are essential readings for everyone interested in physics, and you'll find a copy on the ibraryhelf of every amateur and professional physicist. These lectures are what got me into physics: my astronomy professor told me to read them and see if I liked physics - they changed my life! They are somewhat difficult to understand if you are just getting started, but they will make more and more sense by the time you reach levels 5 and 6 in the undergraduate curriculum.\n- [Deep Down Things: The Breathtaking Beauty of Particle Physics by Bruce Schumm](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F080187971X\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=080187971X&linkCode=as2&tag=susanfowler-20&linkId=6b2ca839cec6cc43cbad403e156c14cf) **(Level: Difficult)**. The very best popular book about particle physics — it clearly explains the most difficult concepts without resorting to speculation. (I had the honor of working with Bruce on a search for supersymmetry at the ATLAS detector.) This book is a great read while you are starting level 7 in the undergraduate curriculum.\n\n### **Mathematical and Scientific Preliminaries**\n\nBefore you begin studying physics and working through the topics in the sections below, you need to be familiar with some basic mathematics. A high school education — which should include pre-algebra, algebra 1, geometry, algebra 2, trigonometry, and pre-calculus — is sufficient. If you need a refresher, I recommend either working through the Khan Academy math courses ([https:\u002F\u002Fwww.khanacademy.org\u002F)](https:\u002F\u002Fwww.khanacademy.org\u002F) or the book [Why Math? by R.D. Driver](https:\u002F\u002Fwww.amazon.com\u002FWhy-Math-Undergraduate-Texts-Mathematics\u002Fdp\u002F0387944273?_encoding=UTF8&amp%3Bqid=&amp%3Bsr=&language=en_US&linkCode=ll1&linkId=0fc3187aa8b5febcc75391ba905635b5&ref_=as_li_ss_tl&tag=susanfowler-20). There's no need to be familiar with calculus before starting, because you’ll learn it as you work through the undergraduate-level courses.\n\nThere are no scientific prerequisites for this curriculum. You don’t need to be familiar with biology or chemistry at either the high school or college level in order to understand, although doing some studying on the side can’t hurt. Khan Academy has some great high school science refresher courses that are perfect for this ([https:\u002F\u002Fwww.khanacademy.org\u002Fscience)](https:\u002F\u002Fwww.khanacademy.org\u002Fscience).\n\n### **How to Study**\n\nEveryone learns very differently, and knowing your learning style is important: do you learn by reading, by taking notes, by talking, by watching, by doing, or by a combination of some or all of these? For example, I learn by reading and by note-taking, so I read through textibrary very carefully, take copious notes, and summarize each concept in my own words before moving on to something new. Think about this before you begin so that you'll know how to structure your studies.\n\nRegardless of your learning style, you'll still need to solve the physics problems in each textbook. **Solving problems is the only way to understand physics.** There's no way around it. Even though it can feel tedious at times, there's nothing more rewarding than figuring out a really difficult physics problem and realizing that you figured it all out all by yourself!\n\nOne tough thing about learning on your own is that you may not know whether you are solving the problems correctly. Some of the textibrary listed below have answers to selected exercises in the back of the book, but these aren’t always adequate for two reasons: (1) they often only show the solutions to the problems, and not the steps taken to get there; and (2) it’s much better to do _all_ of the exercises rather than just a select few. The good news is that many of the solutions (and step-by-step ways to solve them) can be found online with a simple Google search. If you are going to Google the answers, however, _please first try to solve the problems on your own, and try multiple times_ (you’re not in school trying to get a perfect grade — you’re trying to learn and understand).\n\nAnd, finally, a note on learning in a laboratory vs. learning from textibrary. Physics is both an experimental and theoretical science, and while research happens in laboratories and on blackboards and computers, the majority of any physics _education_ does not take place in a laboratory but in lecture classes that teach from textibrary and assign homework problems that are found in textibrary. Yes, there are some laboratory classes (usually at the very introductory levels, and their only purpose is to show that oh, look, Newton’s laws work in the real world after all) and some — _some_ — undergraduates are allowed to participate in research on the side, but physics is taught through textibrary, lectures, and homework problems. Don’t believe me? Take a look at the undergraduate physics curriculum at any university that offers a physics major. Graduate programs in physics are largely the same — both M.A. and PhD programs in physics require two years of core classes — with one key difference: to get a PhD, students need to complete several years of research, a thesis, and — at many programs — take an exam to prove they have mastered the graduate core curriculum. The graduate core curriculum is all textibrary and lectures and homework problems. The textibrary listed in the curriculum I’ve written below are the same textibrary that are used in the top undergraduate and graduate physics programs in the world. Studying them will give you the same education that you would receive at one of these programs — no painfully-annoying-introductory-mechanics-laboratory-class-with-inane-group-projects required.\n\n## **Undergraduate Physics**\n\n### **Overview**\n\nThe curriculum of every undergraduate physics program covers the following subjects (along with some electives in various topics), and usually in the following order:\n\n1. Introduction to Mechanics\n2. Electrostatics\n3. Waves and Vibrations\n4. Modern Physics\n5. Classical Mechanics\n6. Electrodynamics\n7. Quantum Mechanics\n8. Thermodynamics and Statistical Mechanics\n9. Undergraduate Electives\n\nI'm going to cover the details of each of these fields below, including the best textibrary to use and any additional reading you may find helpful in your journey. I'm also going to give some details about the mathematics you'll need to learn alongside each topic.\n\n### **1. Introduction to Mechanics**\n\n**What It's All About**\n\nAn introduction to mechanics course is the first physics class that most people will take in an undergraduate program, and it's the best place to begin independent study of physics as well. This is where you'll start learning how to see the world in mathematical terms. Topics that will be covered: the basics of motion in a straight line, motion in two dimensions, motion in three dimensions, [Newton's Laws](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FNewton%27s_laws_of_motion), [work](\u003Chttps:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FWork_(physics)>), [kinetic energy](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FKinetic_energy), [potential energy](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPotential_energy), [the conservation of energy](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FConservation_of_energy), [momentum](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMomentum), [collisions](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElastic_collision), [rotation and rotational motion](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FRotation_around_a_fixed_axis), [gravitation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FGravity), and periodic motion.\n\n**The Best Textibrary to Use**\n\n- [University Physics with Modern Physics by Young and Freedman](https:\u002F\u002Fwww.amazon.com\u002FUniversity-Physics-Modern-15th-dp-0135159555\u002Fdp\u002F0135159555?language=en_US&linkCode=ll1&linkId=83f94d8e110a2add683656ac03b021c1&ref_=as_li_ss_tl&tag=susanfowler-20) (essential). Work through all of the \"Mechanics\" chapters (in my edition, these are chapters 1-14).This is the best introductory book I've found, and you can use it when you learn electrostatics and modern physics, too. It does a great job of introducing the relevant mathematics, but you'll need to be learning calculus alongside it. There are plenty of great example problems to work through, and the solutions are easy to find online (though you can also buy a [Student Solutions Manual](https:\u002F\u002Fwww.amazon.com\u002FStudent-Solutions-Manual-University-Physics\u002Fdp\u002F0135216958?_encoding=UTF8&language=en_US&linkCode=ll1&linkId=d12dd683b7365eb115eeb59b93966df8&pd_rd_i=0135216958&pd_rd_r=6cbcc49d-5945-4800-862a-f2d9a5664310&pd_rd_w=7KvdQ&pd_rd_wg=xjZRM&pf_rd_p=fd3ebcd0-c1a2-44cf-aba2-bbf4810b3732&pf_rd_r=YVPF9YHJKQGRAK06BWD8&psc=1&refRID=YVPF9YHJKQGRAK06BWD8&ref_=as_li_ss_tl&tag=susanfowler-20)). Please note that you don't need to spend $250 on the new edition — Amazon has lots of copies of [the 12th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321501217\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0321501217&linkCode=as2&tag=susanfowler-20&linkId=5a574e1c2ff846a346c32c7f53955499), [the 13th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321696867\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0321696867&linkCode=as2&tag=susanfowler-20&linkId=ddf424a6eecfcfe35e44d1db6790be82), and the [14th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321973615?ie=UTF8&language=en_US&linkCode=ll1&linkId=0542066c72a562b902ea737105713149&ref_=as_li_ss_tl&tag=susanfowler-20) that contain the same material.\n\n**The Math You'll Need to Learn Alongside It**\n\nYou'll need to learn calculus while working through [University Physics](https:\u002F\u002Fwww.amazon.com\u002FUniversity-Physics-Modern-15th-dp-0135159555\u002Fdp\u002F0135159555?language=en_US&linkCode=ll1&linkId=b29655ef6d618e95cb854f8f9ae55142&ref_=as_li_ss_tl&tag=susanfowler-20)_._ My favorite introductory calculus book is [Thomas' Calculus](https:\u002F\u002Fwww.amazon.com\u002FThomas-Calculus-14th-Joel-Hass-dp-0134438981\u002Fdp\u002F0134438981?language=en_US&linkCode=ll1&linkId=e055fccb0e90aa26395bf8b70ad8eb90&ref_=as_li_ss_tl&tag=susanfowler-20) (you can also use the [earlier](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321587995?ie=UTF8&language=en_US&linkCode=ll1&linkId=a3bf72c1bdee13f41d667b22236fcd0c&ref_=as_li_ss_tl&tag=susanfowler-20) editions), with [Stewart's Calculus](https:\u002F\u002Fwww.amazon.com\u002FCalculus-Early-Transcendentals-James-Stewart-dp-1337613924\u002Fdp\u002F1337613924?language=en_US&linkCode=ll1&linkId=f6ab8fd13d35a55416bd8323a003f1e7&ref_=as_li_ss_tl&tag=susanfowler-20) (older edition [here](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0538497904?ie=UTF8&language=en_US&linkCode=ll1&linkId=2ff44ed10fac5d8dc3431070f7747618&ref_=as_li_ss_tl&tag=susanfowler-20)) coming in as a close second. Work through each chapter, and make sure you can solve problems at the end of each chapter before continuing to the next.\n\nIf you are new to calculus and\u002For find yourself struggling to get accustomed to it, don’t let that stop you. Calculus is really difficult, and it can take a really long time to wrap your head around it. Some things that can help are (1) watching videos like the ones on Khan Academy (\u003Chttps:\u002F\u002Fwww.khanacademy.org\u002F)>, (2) taking [Robert Ghrist’s free calculus courses on Coursera](https:\u002F\u002Fwww.coursera.org\u002Finstructor\u002Frobghrist), and (3) reading a truly amazing little book called [Calculus Made Easy by Silvanus P. Thompson and Martin Gardner](https:\u002F\u002Fwww.amazon.com\u002FCalculus-Made-Easy-Silvanus-Thompson\u002Fdp\u002F0312185480?dchild=1&keywords=calculus&language=en_US&linkCode=ll1&linkId=cd9f2ac14c8ade36fb379691fa162425&qid=1618960480&ref_=as_li_ss_tl&s=library&sr=1-23&tag=susanfowler-20) that breaks everything down really clearly.\n\n### **2. Electrostatics**\n\n**What It's All About**\n\nThis is where you'll learn about the physics of electricity and magnetism ([electromagnetism](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectromagnetism)) in static situations (situations where no motion is involved). Topics covered are: [electric charges](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectric_charge) and [electric fields](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectric_field), [magnetism](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMagnetism) and [magnetic fields](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMagnetic_field), [Gauss's Law](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FGauss%27s_law), [capacitance](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCapacitance), [resistance and conductance](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectrical_resistance_and_conductance), [inductance](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FInductance), [current](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectric_current), and how [circuits work](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectrical_network).\n\n**The Best Textibrary to Use**\n\n- [University Physics with Modern Physics by Young and Freedman](https:\u002F\u002Fwww.amazon.com\u002FUniversity-Physics-Modern-15th-dp-0135159555\u002Fdp\u002F0135159555?language=en_US&linkCode=ll1&linkId=1e49ffb9f18ac271717679c9c76826d1&ref_=as_li_ss_tl&tag=susanfowler-20) (essential). Work through the chapters on \"Electromagnetism\" (in my edition, these are chapters 21-32). You can find inexpensive copies of [the 12th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321501217\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0321501217&linkCode=as2&tag=susanfowler-20&linkId=5a574e1c2ff846a346c32c7f53955499), [the 13th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321696867\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0321696867&linkCode=as2&tag=susanfowler-20&linkId=ddf424a6eecfcfe35e44d1db6790be82), and the [14th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321973615?ie=UTF8&language=en_US&linkCode=ll1&linkId=0542066c72a562b902ea737105713149&ref_=as_li_ss_tl&tag=susanfowler-20) that contain the same material.\n\n**The Math You'll Need To Learn Alongside It**\n\nKeep working through the calculus textibrary ([Thomas](https:\u002F\u002Fwww.amazon.com\u002FThomas-Calculus-14th-Joel-Hass-dp-0134438981\u002Fdp\u002F0134438981?language=en_US&linkCode=ll1&linkId=d72cf5af7a3e077a3deb9bb2556886e9&ref_=as_li_ss_tl&tag=susanfowler-20) or [Stewart](https:\u002F\u002Fwww.amazon.com\u002FCalculus-Early-Transcendentals-James-Stewart-dp-1337613924\u002Fdp\u002F1337613924?language=en_US&linkCode=ll1&linkId=260314dde4baac0f191ee371e799ad18&ref_=as_li_ss_tl&tag=susanfowler-20)) while you work through the basics of electrostatics, but you should finish them by the time you finish the electromagnetism chapters in [University Physics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321973615\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0321973615&linkCode=as2&tag=susanfowler-20&linkId=4724b43f949f1f5295f91dd9b2c1c3f5). You absolutely must understand the basics of calculus before you move on to the other topics in physics.\n\n### **3. Waves and Vibrations**\n\n**What It's All About**\n\nThe mechanics of vibrations and waves are complex and important enough to demand their own course of study. Mastering this material is essential for learning about quantum mechanics, so don't skip this topic! This is where you will learn about [simple harmonic oscillators](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSimple_harmonic_motion), damped harmonic oscillators, forced oscillations, coupled oscillators, [waves](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FWave), [interference](\u003Chttps:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FInterference_(wave_propagation)>), [diffraction](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FDiffraction), and [dispersion](\u003Chttps:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FDispersion_(optics)>).\n\n**The Best Textibrary to Use**\n\n- [Vibrations and Waves by French](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F8123909144\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=8123909144&linkCode=as2&tag=susanfowler-20&linkId=3c5b0fa433139f20155050ceda42688d) (essential) and [Vibrations and Waves by King](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0470011890\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0470011890&linkCode=as2&tag=susanfowler-20&linkId=1c37debf5e2966c4b29cd7f4bb3243f0) (essential). These two library complement each other very well, and contain different problems and solutions.\n\n**The Math You'll Need To Learn Alongside It**\n\nBy this point, you should have finished the introductory calculus library and are ready to move on to more advanced mathematics. You should start working through [Zill's Advanced Engineering Mathematics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB01LZ8LP3M?language=en_US&linkCode=ll1&linkId=601bfe2c0d757c3f265df6c3bc151b63&ref_=as_li_ss_tl&tag=susanfowler-20), which is a thoroughintroduction to more advanced topics in mathematics (linear algebra, complex analysis, real analysis, partial differential equations, and ordinary differential equations). The topics in this book are essential — once you master them, you'll have all the math you need to know in order to understand undergraduate physics. You can also buy the (cheaper) [4th](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0763779660?ie=UTF8&language=en_US&linkCode=ll1&linkId=9264ee7f5b4c8774ee0fc37b951aa5c4&ref_=as_li_ss_tl&tag=susanfowler-20) and [5th editions](https:\u002F\u002Fwww.amazon.com\u002FAdvanced-Engineering-Mathematics-Dennis-Zill\u002Fdp\u002F1449691722?dchild=1&keywords=Advanced%20Engineering%20Mathematics%205th%20Edition&language=en_US&linkCode=ll1&linkId=b2837bef42bb63b24435ac2a398a475b&qid=1618961790&ref_=as_li_ss_tl&s=library&sr=1-6&tag=susanfowler-20).\n\n### **4. Modern Physics**\n\n**What It's All About**\n\nThe fourth physics class that most undergraduates take is usually called \"Modern Physics\", and it's an introduction to topics in physics that will be taught in greater detail later in the undergraduate physics curriculum. If you plan to study the advanced topics on their own, it's fine to skip this class, but covering these topics now in your independent studies will allow you to grasp the advanced topics that you hear so much about and that probably got you into physics in the first place. This is where you'll learn the basics of [thermodynamics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FThermodynamics), [relativity](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSpecial_relativity), [quantum mechanics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuantum_mechanics), [atomic physics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAtomic_physics), [nuclear physics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FNuclear_physics), [particle physics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FParticle_physics), and [cosmology](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCosmology).\n\n**The Best Textibrary to Use**\n\n- [University Physics with Modern Physics by Young and Freedman](https:\u002F\u002Fwww.amazon.com\u002FUniversity-Physics-Modern-15th-dp-0135159555\u002Fdp\u002F0135159555?language=en_US&linkCode=ll1&linkId=04a833d493c86c6c03323c689abc6192&ref_=as_li_ss_tl&tag=susanfowler-20) (essential). Work through the \"Thermodynamics\" section (chapters 17-20 in my edition of the book), and the \"Modern Physics\" section (chapters 37-44). You can find inexpensive copies of [the 12th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321501217\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0321501217&linkCode=as2&tag=susanfowler-20&linkId=5a574e1c2ff846a346c32c7f53955499), [the 13th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321696867\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0321696867&linkCode=as2&tag=susanfowler-20&linkId=ddf424a6eecfcfe35e44d1db6790be82), and the [14th edition](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0321973615?ie=UTF8&language=en_US&linkCode=ll1&linkId=0542066c72a562b902ea737105713149&ref_=as_li_ss_tl&tag=susanfowler-20) that contain the same material.\n\n**The Math You'll Need To Learn Alongside It**\n\nContinue working through [Zill's Advanced Engineering Mathematics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB01LZ8LP3M?language=en_US&linkCode=ll1&linkId=601bfe2c0d757c3f265df6c3bc151b63&ref_=as_li_ss_tl&tag=susanfowler-20). Once you have mastered all of the topics in this book, you'll have all the math you need to know in order to understand undergraduate physics.\n\n### **5. Classical Mechanics**\n\n**What It's All About**\n\nThis is where you’ll _really_ learn classical mechanics, which you were introduced to in the very first course (Introduction to Mechanics). You'll study the topics in much greater depth, and learn how to use different mathematical formalisms of classical mechanics (the [Lagrangian formalism](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FLagrangian_mechanics) and the [Hamiltonian formalism](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FHamiltonian_mechanics)) to solve problems in mechanics.\n\n**The Best Textibrary to Use**\n\n- [Taylor's Classical Mechanics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F189138922X\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=189138922X&linkCode=as2&tag=susanfowler-20&linkId=a6a0cb5612e181573e9c4348a07ebce4) (essential). This is a fantastic introduction to classical mechanics.\n- [Morin's Introduction to Classical Mechanics with Problems and Solutions](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0521876222\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0521876222&linkCode=as2&tag=susanfowler-20&linkId=3ebbc6ab7b785fe7868e52fdfb4dd2ec) (supplement). Morin's book is a good supplement to Taylor's, and contains some great problems to work through.\n- [Problems and Solutions in Introductory Mechanics by Morin](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F1482086921\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1482086921&linkCode=as2&tag=susanfowler-20&linkId=07ada7370585958f9a953c14a6d7b776) (supplement). Even more great problems (with solutions) to work through, and contains some great problem-solving strategies.\n\n**The Math You'll Need To Learn Alongside It**\n\nIf you haven't finished working through [Zill](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB01LZ8LP3M?language=en_US&linkCode=ll1&linkId=601bfe2c0d757c3f265df6c3bc151b63&ref_=as_li_ss_tl&tag=susanfowler-20) by now, you should master the topics in it by the time you finish studying classical mechanics.\n\n### **6. Electrodynamics**\n\n**What It's All About**\n\nEarlier, you learned about electrostatics: the study of static (non-moving) electricity and magnetism. By now, you know the mathematics to understand [electrodynamics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FClassical_electromagnetism), which encompasses everything about classical electricity and magnetism. You'll cover [electrostatics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectrostatics) again, then learn about [Laplace's equation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FLaplace%27s_equation), [multipole expansions](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMultipole_expansion), [polarization](\u003Chttps:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPolarization_(waves)>), [dielectrics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FDielectric), the [Lorentz Force Law](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FLorentz_force), the [Biot-Savart Law](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FBiot%E2%80%93Savart_law), [magnetic vector potential](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMagnetic_potential#Magnetic_vector_potential), [electromotive force](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectromotive_force), [electromagnetic induction](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectromagnetic_induction), [Maxwell's equations](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMaxwell%27s_equations), [electromagnetic waves and radiation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectromagnetic_radiation), and [special relativity](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSpecial_relativity).\n\n**The Best Textibrary to Use**\n\n- [Griffith's Introduction to Electrodynamics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F8120347765\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=8120347765&linkCode=as2&tag=susanfowler-20&linkId=31461e6adfc67af2ca9f6767492794cb) (essential). This is _the_ book on undergraduate electrodynamics and one of the very best physics textibrary ever written. Make sure you work through _every single problem_ in the book.\n- [Div, Grad, Curl and All That by Schey](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0393925161\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0393925161&linkCode=as2&tag=susanfowler-20&linkId=65aecc9d2596cb020ed8b46152bfc883) (supplement). This is a short textbook on vector calculus that is very helpful when trying to work with vectors in electrodynamics.\n- [A Student's Guide to Maxwell's Equations by Fleisch](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0521701473\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0521701473&linkCode=as2&tag=susanfowler-20&linkId=a274a62e927aa70484cbb340db31c860) (supplement). Maxwell's equations are essential in understanding electrodynamics, and this book is the best supplement on the topic.\n\n### **7. Quantum Mechanics**\n\n**What It's All About**\n\nBy this point, you're ready to really dive into the fundamentals of [quantum mechanics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuantum_mechanics) and its applications — one of the most beautiful, interesting, and thought-provoking topics in all of physics. You'll learn to see the world in a completely new way. You'll learn about the [wave function](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FWave_function), [the Schrodinger equation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSchr%C3%B6dinger_equation), [perturbation theory,](\u003Chttps:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPerturbation_theory_(quantum_mechanics)>) the [variational principle](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FVariational_principle), the [WKB Approximation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FWKB_approximation), the [adiabatic approximation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAdiabatic_theorem), and [scattering](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FScattering_theory).\n\n**The Best Textibrary to Use**\n\n- [Griffith's Introduction to Quantum Mechanics](https:\u002F\u002Fwww.amazon.com\u002FIntroduction-Quantum-Mechanics-David-Griffiths-dp-1107189632\u002Fdp\u002F1107189632?language=en_US&linkCode=ll1&linkId=c319e9c4889ef4c55ba19d3adbc7512c&ref_=as_li_ss_tl&tag=susanfowler-20) (essential). This is, without a doubt, _the_ book on undergraduate quantum mechanics, written by the same Griffiths who wrote the [Introduction to Electrodynamics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F8120347765\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=8120347765&linkCode=as2&tag=susanfowler-20&linkId=31461e6adfc67af2ca9f6767492794cb). It's written in the same concise and beautiful style, and every single problem is worth solving.\n\n### **8. Thermodynamics and Statistical Mechanics**\n\n**What It's All About**\n\n[Thermodynamics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FThermodynamics) is the field of physics concerned with kinetics (dynamics) related to heat and energy, while [statistical mechanics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FStatistical_mechanics) is all about the microscopic principles that underlie the [Laws of Thermodynamics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FLaws_of_thermodynamics). This is where you'll learn about the [laws of thermodynamics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FLaws_of_thermodynamics), [entropy](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FEntropy), the [canonical ensemble](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCanonical_ensemble), [Maxwell distributions](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMaxwell%E2%80%93Boltzmann_distribution), [Planck's distribution](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPlanck%27s_law), [Fermi-Dirac statistics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FFermi%E2%80%93Dirac_statistics), [Bose-Einstein statistics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FBose%E2%80%93Einstein_statistics), and [phase transitions](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPhase_transition).\n\nBy the time you've finished this topic, you'll have mastered all of the fundamentals of undergraduate physics!\n\n**The Best Textibrary to Use**\n\n- [Schroeder’s An Introduction to Thermal Physics ](https:\u002F\u002Fwww.amazon.com\u002FIntroduction-Thermal-Physics-Daniel-Schroeder\u002Fdp\u002F0201380277?language=en_US&linkCode=ll1&linkId=83111d396110c7cfd24820446d826528&pd_rd_i=0201380277&pd_rd_r=f7733715-77d8-46d9-872e-01036734e3c1&pd_rd_w=ETVhr&pd_rd_wg=kPD2d&pf_rd_p=8019ba47-0a12-4976-b76b-5c932d60db6f&pf_rd_r=3RW65PM2JXHNYRQP93NA&psc=1&ref_=as_li_ss_tl&tag=susanfowler-20)(essential). A very thorough and comprehensive introduction to thermodynamics and statistical mechanics; contains very clear and straightforward explanations and examples.\n- [Introductory Statistical Mechanics by Bowley and Sanchez](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0198505760\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0198505760&linkCode=as2&tag=susanfowler-20&linkId=6946245b927cee4f04ca6bfda30d2e79) (supplement). A good second text to have on hand to reference.\n\n### **9. Undergraduate Electives**\n\n**What They’re All About**\n\nNow that you understand all of the fundamentals of undergraduate physics, you have a solid foundation and can study more advanced and specialized topics, including (but not limited to) [astronomy](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAstronomy), [astrophysics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAstrophysics), [biophysics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FBiophysics), [cosmology](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCosmology), [electronics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectronics), [optics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FOptics), [particle physics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FParticle_physics), and [string theory](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FString_theory).\n\n**The Best Textibrary to Use**\n\n- **Astronomy:** [The Cosmic Perspective](https:\u002F\u002Fwww.amazon.com\u002FCosmic-Perspective-9th-Jeffrey-Bennett-dp-0134874366\u002Fdp\u002F0134874366?language=en_US&linkCode=ll1&linkId=a32b07d7561f2bf9ee64155bbdddad09&ref_=as_li_ss_tl&tag=susanfowler-20). A wonderful introduction to astronomy, accessible to anyone who is just beginning to study physics.\n- **Astrophysics:** [An Introduction to Modern Astrophysics by Carroll and Ostlie](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0805304029\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0805304029&linkCode=as2&tag=susanfowler-20&linkId=be2a1be4e50f0c30670e7aa6511b2c42). A comprehensive introduction to modern astrophysics.\n- **Biophysics:** [Biophysics: An Introduction by Glaser](https:\u002F\u002Fwww.amazon.com\u002FBiophysics-Introduction-Roland-Glaser-ebook\u002Fdp\u002FB00A9YGFBK?dchild=1&keywords=biophysics&language=en_US&linkCode=ll1&linkId=0d178033fed0db3517767cf569fb8bd1&qid=1618966016&ref_=as_li_ss_tl&s=library&sr=1-5&tag=susanfowler-20). A solid introduction to the principles of biophysics.\n- **Cosmology:** [Ryden's Introduction to Cosmology](https:\u002F\u002Fwww.amazon.com\u002FIntroduction-Cosmology-Barbara-Ryden-dp-1107154839\u002Fdp\u002F1107154839?language=en_US&linkCode=ll1&linkId=686d9b29f7b225fba87b9f920ca3df7b&ref_=as_li_ss_tl&tag=susanfowler-20). My absolute favorite introductory cosmology book.\n- **Electronics:** [Basic Electronics for Scientists and Engineers by Eggleston](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0521154308\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0521154308&linkCode=as2&tag=susanfowler-20&linkId=eaa933ffc178dc52f52da6c347e8c4ea). Accessible to anyone who has worked through the basics of electrodynamics.\n- **Optics.** [Optics by Hecht](https:\u002F\u002Fwww.amazon.com\u002FOptics-5th-Eugene-Hecht\u002Fdp\u002F0133977226?_encoding=UTF8&language=en_US&linkCode=ll1&linkId=d38230d12a814b81abb8a8b5201ebb99&qid=1618965492&ref_=as_li_ss_tl&sr=1-1&tag=susanfowler-20). The classic (and truly amazing) optics textbook.\n- **Particle Physics**: [Griffith's Introduction to Elementary Particles](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F3527406018\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=3527406018&linkCode=as2&tag=susanfowler-20&linkId=90b30a3f4e6b7dd629a631cb7815d5ea). Written by the same Griffith who gave us the [Introduction to Electrodynamics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F8120347765\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=8120347765&linkCode=as2&tag=susanfowler-20&linkId=31461e6adfc67af2ca9f6767492794cb) and[ Introduction to Quantum Mechanics](https:\u002F\u002Fwww.amazon.com\u002Fdp\u002FB07G15LW25?language=en_US&linkCode=ll1&linkId=fe0ac80a7bb24ae45b77018743207f11&pd_rd_i=B07G15LW25&pd_rd_r=0e5f245f-2014-4529-ad94-c176004d7189&pd_rd_w=kD7KX&pd_rd_wg=IfFtV&pf_rd_p=085568d9-3b13-4ac1-8ae4-24a26c00cb0c&pf_rd_r=9FCHHBWK0SM6YCC136MT&psc=1&ref_=as_li_ss_tl&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEzMUo4SzZUOVJGWjVXJmVuY3J5cHRlZElkPUEwODE3MDM2MUxYNEkwN1FEQVpKNCZlbmNyeXB0ZWRBZElkPUEwODc1MTUzTk45QzQ5RzEzVEowJndpZGdldE5hbWU9c3BfZGV0YWlsJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ%3D%3D&tag=susanfowler-20), this book is the perfect introduction to the fundamentals of particle physics and is a joy to work through.\n- **String Theory.** [A First Course in String Theory by Zwiebach](https:\u002F\u002Fwww.amazon.com\u002FFirst-Course-String-Theory-2nd\u002Fdp\u002F0521880327?dchild=1&keywords=string%20theory&language=en_US&linkCode=ll1&linkId=56d954f30bd8fefd220f1c853389f224&qid=1618965203&ref_=as_li_ss_tl&s=library&sr=1-6&tag=susanfowler-20). The essential introduction to string theory.\n\n### **Graduate Physics**\n\n### **Overview**\n\nGraduate-level physics requires mastery of every topic within the undergraduate physicscurriculum above as a prerequisite.\n\nThe graduate physics core is comprised of:\n\n1. Mathematical Methods in Physics\n2. Electrodynamics\n3. Quantum Mechanics\n4. Statistical Mechanics\n5. General Relativity\n6. Quantum Field Theory\n7. Graduate Electives\n\nI'll cover each of these in the sections below. (Note: many graduate students are required to take a course in classical mechanics as part of the graduate core, but if you've mastered the material in undergraduate classical mechanics there is no need for this).\n\n### **1. Mathematical Methods in Physics**\n\n**What It's All About**\n\nStudying electrodynamics, quantum mechanics, and stat mech in more depth at the graduate level requires a greater level of mathematical rigor. To prepare, you'll need to learn the following in greater detail: [Fourier analysis](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FFourier_analysis), [tensors](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FTensor), [ODEs](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FOrdinary_differential_equation), [PDEs](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPartial_differential_equation), [real analysis](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FReal_analysis), [complex analysis](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FComplex_analysis), [algebra](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAlgebra#Abstract_algebra), and [group theory](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FGroup_theory) (to name a few).\n\n**The Best Textibrary To Use**\n\n- [Mathematical Methods for Physicists by Arfken, Weber, and Harris](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0123846544\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0123846544&linkCode=as2&tag=susanfowler-20&linkId=8245a50e135a8ddf5c7249a0ecfce4b3) (essential). This book covers the essentials of everything you'll need to know for the mathematical rigor demanded by the graduate core.\n- [Tolstov's Fourier Series](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0486633179\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0486633179&linkCode=as2&tag=susanfowler-20&linkId=47cef211064681ee48165c8be7e0a518) (supplement). The best book on Fourier Analysis ever written. Complements the main text very well.\n- [Complex Variables by Fisher](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0486406792\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0486406792&linkCode=as2&tag=susanfowler-20&linkId=6498db95d42cc4d3b3f1cf36c4e49def) (supplement). Amazing overview of complex analysis. Can be used along with [Needham's Visual Complex Analysis](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0198534469\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0198534469&linkCode=as2&tag=susanfowler-20&linkId=51c923a6d2da55c26ae67231ec7e854b) to supplement the main text.\n- [Zee's Group Theory in a Nutshell for Physicists](https:\u002F\u002Fsusan-fowler-b4lr.squarespace.com\u002Fblog\u002F2016\u002F8\u002F13\u002F%3Cahref=%22https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0691162697\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0691162697&linkCode=as2&tag=susanfowler-20&linkId=edd23dac43d4fe8ffa9f411fe2923e20%22%3EGroup%20Theory%20in%20a%20Nutshell%20for%20Physicists%3C\u002Fa%3E%3Cimg%20src=%22\u002F\u002Fir-na.amazon-adsystem.com\u002Fe\u002Fir?t=susanfowler-20&l=am2&o=1&a=0691162697%22%20width=%221%22%20height=%221%22%20border=%220%22%20alt=%22%22%20style=%22border:none%20!important;%20margin:0px%20!important;%22%20\u002F%3E) (supplement). A brilliant introduction to group theory for physicists.\n\n### **2. Graduate Electrodynamics**\n\n**What It's All About**\n\nGraduate-level electrodynamics covers the same topics as undergraduate electrodynamics but with greater mathematical rigor.\n\n**The Best Textibrary To Use**\n\n- [Classical Electrodynamics by Jackson](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F047130932X\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=047130932X&linkCode=as2&tag=susanfowler-20&linkId=9bd8aaea20913478d4cb514f91ed0929) (essential). This is the bible of classical electrodynamics, and everyone who works through either loves it or hates it (I loved it). If you can master everything in this book and work through a decent selection of the problems, you'll have mastered electrodynamics.\n\n### **3. Graduate Quantum Mechanics**\n\n**What It's All About**\n\nGraduate quantum mechanics is far more advanced than what you learned at the undergraduate level. Here you'll learn, in great depth, all there is to know about quantum mechanics, including [quantum dynamics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuantum_dynamics) (the [Schrodinger equation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSchr%C3%B6dinger_equation), the [Heisenberg picture](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FHeisenberg_picture), [propagators](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPropagator), and [Feynman path integrals](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPath_integral_formulation)), [angular momentum](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAngular_momentum_operator), [symmetries](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSymmetry_in_quantum_mechanics) and [conservation laws](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FNoether%27s_theorem) of the quantum world, [perturbation theory](\u003Chttps:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPerturbation_theory_(quantum_mechanics)>), [scattering theory](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FScattering_theory), [relativistic quantum mechanics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FRelativistic_quantum_mechanics), [decoherence](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuantum_decoherence), and [interpretations of quantum mechanics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FInterpretations_of_quantum_mechanics) (the [Copenhagen](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCopenhagen_interpretation) vs. [Many-Worlds](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FMany-worlds_interpretation) interpretations).\n\n**The Best Textibrary To Use**\n\n- [Sakurai's Modern Quantum Mechanics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB00DT62BOA\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B00DT62BOA&linkCode=as2&tag=susanfowler-20&linkId=9b659e22baeb85c6f477c3eabe9c3c62) (essential). This is my favorite textbook on quantum mechanics, and the one I used to learn quantum mechanics for the very first time. It's a wonderful, elegant, simple book with clear and understandable problems. Try to work through all of the problems — if you do, you'll understand quantum mechanics very well.\n- [Quantum Mechanics and Path Integrals by Feynman](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0486477223\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0486477223&linkCode=as2&tag=susanfowler-20&linkId=0c7d421cfd3dde2410cfba580311cb68) (essential). Sakurai's coverage of Feynman's Path Integral formalism of quantum mechanics doesn't do it justice. Working through this text (written by Feynman himself) is not only useful, but incredibly fun.\n- [The Principles of Quantum Mechanics by Dirac](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0198520115\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0198520115&linkCode=as2&tag=susanfowler-20&linkId=ee9f05b4a8a41117dd4c35b7c38b754f) (supplement). [Dirac](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPaul_Dirac) was one of the founding fathers of quantum mechanics and quantum field theory. This book is important historically, and also will open your eyes to the need for quantum field theory.\n- [Principles of Quantum Mechanics by Shankar](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0306447908\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0306447908&linkCode=as2&tag=susanfowler-20&linkId=c5ba6aff751d9f50c766cc259b5e2d86) (supplement). A great supplement to Sakurai for more information about each topic. A bit too dense to serve as a primary text, it works best as an addition or reference.\n- [Decoherence and the Appearance of a Classical World in Quantum Theory](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F3540003908\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=3540003908&linkCode=as2&tag=susanfowler-20&linkId=667e93b91dd9ef0d96093f56e8cf53ad) (supplement). This book is very dense and you may not understand all of it even after working through Sakurai, but understanding decoherence is essential to understanding how the classical world arises from the quantum.\n- [The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0691145075\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0691145075&linkCode=as2&tag=susanfowler-20&linkId=95fbf3134a7de58e63387b524b049231) (supplement). Very few library have been written on interpretations of quantum mechanics, and reading through this volume helps to understand the limitations of our interpretations as well as the complexities and details of Everett's Many-Worlds interpretation.\n\n### **4. Graduate Statistical Mechanics**\n\n**What It's All About**\n\nNow that you have a more solid mathematical background and understand all of the fundamentals of quantum mechanics, it's time to approach graduate-level statistical mechanics. You'll revisit the Laws of Thermodynamics, and then pick up from where you left off in undergraduate statistical mechanics.\n\n**The Best Textibrary To Use**\n\n- [Statistical Mechanics by Pathria and Beale](https:\u002F\u002Fwww.amazon.com\u002FStatistical-Mechanics-R-K-Pathria-dp-0081026927\u002Fdp\u002F0081026927?language=en_US&linkCode=ll1&linkId=7a78e10e8bd40958087e50734c8b79f2&ref_=as_li_ss_tl&tag=susanfowler-20) (essential). This book is, admittedly, a bit frustrating, but it's worth suffering through because if you make it all the way to the end and work through the majority of the problems, you'll know stat mech like the back of your hand.\n- [Huang's Statistical Mechanics](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0471815187\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0471815187&linkCode=as2&tag=susanfowler-20&linkId=189688411c439ed695b3ccd1622c7f54) (supplementary). This is a great book to supplement the main text — is a good bridge between undergraduate stat mech and Pathria.\n\n### **5. General Relativity**\n\n**What It's All About**\n\nBy now you'll have a very deep understanding of [Einstein's special theory of relativity](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSpecial_relativity), but, as you may have noticed, [general relativity](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FGeneral_relativity) (GR) — the theory of gravitation — hasn't yet been mentioned. That's because GR is a mathematically demanding topic — not only do you need to know all of the math you've learned so far,  but you'll need to learn [differential geometry](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FDifferential_geometry) in order to make sense of how gravity works. Here, you'll revisit [special relativity](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSpecial_relativity) and the intricacies of [spacetime](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSpacetime), then learn the basics of [differential geometry](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FDifferential_geometry), how to deal with [curvature](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCurvature), the essentials of [gravitation](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FIntroduction_to_general_relativity), how [black holes](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FBlack_hole) work, and the basics of [cosmology](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCosmology).\n\n**The Best Textibrary To Use**\n\n- [Spacetime and Geometry by Carroll ](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0805387323\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0805387323&linkCode=as2&tag=susanfowler-20&linkId=76a009803af6c128e44f312b0fd4f30f)(essential). This is _the_ book on general relativity, and Carroll does a phenomenal job of introducing the essentials of differential geometry and general relativity.\n- [Einstein Gravity in a Nutshell by Zee](https:\u002F\u002Fwww.amazon.com\u002FEinstein-Gravity-Nutshell-Zee\u002Fdp\u002F069114558X?_encoding=UTF8&language=en_US&linkCode=ll1&linkId=e895d4616875cecf3c27ab0e021747ab&pd_rd_i=069114558X&pd_rd_r=5315ce76-2a4d-4af1-b8f4-d1f5ee809a02&pd_rd_w=Lp44k&pd_rd_wg=OWaie&pf_rd_p=fd3ebcd0-c1a2-44cf-aba2-bbf4810b3732&pf_rd_r=J4YF21VX61B9QBZWE3VD&psc=1&refRID=J4YF21VX61B9QBZWE3VD&ref_=as_li_ss_tl&tag=susanfowler-20) (supplement). A great, accessible overview.\n- [Wald's General Relativity](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0226870332\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0226870332&linkCode=as2&tag=susanfowler-20&linkId=e5ad192d5237867ba093c6533030d0ac) (supplement). Wald's book is a very abstract, high-level overview of general relativity, and makes a great supplement to Carroll's book. Go to Carroll for the overview, look it up in Wald for the high-level abstractions, and then look in the [apple book](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0716703440\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0716703440&linkCode=as2&tag=susanfowler-20&linkId=0f202faba0a99e956251024296be2b33) for the dirty details.\n- [Gravitation by Misner, Thorne, and Wheeler](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0716703440\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0716703440&linkCode=as2&tag=susanfowler-20&linkId=0f202faba0a99e956251024296be2b33) (supplement). Also known as the \"apple book\" thanks to the apple gracing its cover, this book goes into the nitty-gritty details of general relativity in ways that no other book does.\n- [Weinberg's Gravitation and Cosmology](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB008VRVK44\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B008VRVK44&linkCode=as2&tag=susanfowler-20&linkId=2b86a141434b6399cb2ff39bea63bb29) (supplement). Weinberg is one of those rare physicists who has not only been at the forefront of every major field in physics, but has written about each of them as well. His library tend to be inaccessible to beginners, however, and this book is no exception. It does make a good supplementary reading, but I'd advise reading it after you've worked through the rest.\n- [Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo](https:\u002F\u002Fwww.amazon.com\u002FDifferential-Geometry-Curves-Surfaces-Mathematics-ebook\u002Fdp\u002FB01NCHYI33?language=en_US&linkCode=ll1&linkId=b990005bdae7f2acf283118e637fc241&pd_rd_i=B01NCHYI33&pd_rd_r=2f8b30eb-52e9-4d68-be57-85266802700e&pd_rd_w=nnUNY&pd_rd_wg=OznzN&pf_rd_p=78971f67-4c78-4f07-b5c1-ee9acd72068c&pf_rd_r=XSE51QVTY28WEJEM35GP&psc=1&ref_=as_li_ss_tl&tag=susanfowler-20) (supplement). The classic differential geometry textbook; may be useful to help you wrap your head around differential geometry.\n\n### **6. Quantum Field Theory**\n\n**What It's All About**\n\nQuantum Field Theory (QFT) is the heart of all modern high-energy physics: the Standard Model of particle physics is a QFT. The whole idea behind QFT is that we are doing quantum mechanics on classical fields, and it works remarkably well. Along with GR, QFT will be the most challenging part of your physics education, but perhaps the most rewarding (I know it was extraordinarily rewarding for me!). It may take many, many years to master. You'll learn about how to [quantize fields](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSecond_quantization), [Feynman diagrams](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FFeynman_diagram), [quantum electrodynamics (QED)](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuantum_electrodynamics), [renormalization](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FRenormalization), [non-Abelian gauge theories](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FGauge_theory), [quantum chromodynamics (QCD)](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuantum_chromodynamics), [the Higgs mechanism](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FHiggs_mechanism), [the Glashow-Weinberg-Salam theory](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectroweak_interaction) of electroweak interactions, the [symmetries of particle physics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FStandard_Model), and [spontaneous symmetry breaking](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSpontaneous_symmetry_breaking).\n\n**The Best Textibrary To Use**\n\n- [Zee's Quantum Field Theory in a Nutshell](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0691140340\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0691140340&linkCode=as2&tag=susanfowler-20&linkId=1f7f650184687b5ba35fc46366c61763) (essential). This is my favorite physics book of all time, and the most beautiful introduction to QFT ever written. You'll walk away understanding the basics of QFT and with a deep understanding of the fundamental nature of the universe.\n- [An Introduction to Quantum Field Theory by Peskin and Schroeder](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0201503972\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0201503972&linkCode=as2&tag=susanfowler-20&linkId=50a9dbc88d7e01dbd5ea8a78b8f5a0e0) (essential). This is the bible of QFT, but its far too terse and encyclopedic to work through on its own and must be studied alongside Zee. Covers everything you could possibly want to know about QFT. Try to work through the problems, but be aware that mastery of QFT will take a very, very long time.\n- [Weinberg's The Quantum Theory of Fields, Volume 1](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0521550017\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0521550017&linkCode=as2&tag=susanfowler-20&linkId=8aad9a648a91c5c2a1813ae01d44ad30) (supplement). Another great volume by Weinberg, who was one of the most important physicists in the history of particle physics. This book should be used only as a supplement, and preferably not read until Zee and Peskin and Schroeder have been completed. It's not a book to learn from, but one to gain additional understanding of QFT through after you've mastered all of the basics.\n- [Lie Algebras in Particle Physics by Georgi](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002F0738202339\u002Fref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0738202339&linkCode=as2&tag=susanfowler-20&linkId=8768c4b53df08da4c985b159901715e3) (supplement). This dives into the details of Lie Algebras in QFT.\n\n### **7. Graduate Electives**\n\n**What They’re All About**\n\nThe graduate curriculum can be split into several categories: (i) the core courses, (ii) specialized coursework and graduate electives, and (iii) research. Graduate students typically take the core courses first, which focus on the same topics covered in undergraduate courses but in much greater depth and with far more mathematical rigor. Students then choose more specialized courses and electives depending on their area of research in physics, including (but not limited to) [condensed matter physics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCondensed_matter_physics), [cosmology](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCosmology), [electronics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FElectronics), [optics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FOptics), [particle physics](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FParticle_physics), [quantum computing](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuantum_computing), [solid-state physics,](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSolid-state_physics) and [string theory](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FString_theory).\n\n**The Best Textibrary to Use**\n\n- **Condensed Matter Physics:** [Lubensky’s Principles of Condensed Matter Physics](https:\u002F\u002Fwww.amazon.com\u002FPrinciples-Condensed-Matter-Physics-Chaikin\u002Fdp\u002F0521794501?dchild=1&keywords=lubensky%20condensed%20matter&language=en_US&linkCode=ll1&linkId=7bc228f55f58c7928e37da7c99ae1278&qid=1618980102&ref_=as_li_ss_tl&sr=8-1&tag=susanfowler-20). A modern, comprehensive textbook. Fairly advanced, and is easier to understand after completing the graduate core and working through something like [Ashcroft and Mermin](https:\u002F\u002Fwww.amazon.com\u002FSolid-State-Physics-Neil-Ashcroft\u002Fdp\u002F8131500527?crid=2S8RO77XRYDXS&dchild=1&keywords=ashcroft%20and%20mermin%20solid%20state%20physics&language=en_US&linkCode=ll1&linkId=ed543039975467b23595195e55fcdaaf&qid=1618977068&ref_=as_li_ss_tl&sprefix=ashcroft%20and%20mer%2Cdigital-text%2C222&sr=8-1&tag=susanfowler-20).\n- **Cosmology:** Mark Trodden and Sean Carroll’s [TASI Lectures: Introduction to Cosmology](https:\u002F\u002Farxiv.org\u002Fabs\u002Fastro-ph\u002F0401547). Supplement with [Steven Weinberg’s Cosmology](https:\u002F\u002Fwww.amazon.com\u002FCosmology-Steven-Weinberg\u002Fdp\u002F0198526822?dchild=1&keywords=cosmology&language=en_US&linkCode=ll1&linkId=0c4cf65f17f6f9b1e2c14c6bfab29d24&qid=1619026039&ref_=as_li_ss_tl&s=library&sr=1-6&tag=susanfowler-20).\n- **Electronics:** [The Art of Electronics by Horowitz and Hill](https:\u002F\u002Fwww.amazon.com\u002Fdp\u002F0521809266?language=en_US&linkCode=ll1&linkId=406668d01de865aeb3ce4aecf4b85a08&pd_rd_i=0521809266&pd_rd_r=b7f975c9-cefd-47f6-a780-b79087dbd3ee&pd_rd_w=YKMDW&pd_rd_wg=pz6EU&pf_rd_p=085568d9-3b13-4ac1-8ae4-24a26c00cb0c&pf_rd_r=V086395H90KBSAZGBNC4&psc=1&ref_=as_li_ss_tl&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEyWlJaMlVIT0RJT05HJmVuY3J5cHRlZElkPUEwMDk3NTA2MUE5SU1QWFM5M1NITyZlbmNyeXB0ZWRBZElkPUEwNDY1MTgyMUJJU0JXUk1WUTcwSiZ3aWRnZXROYW1lPXNwX2RldGFpbCZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU%3D&tag=susanfowler-20). The best electronics textbook there is, period.\n- **Optics:** [Optics by Hecht](https:\u002F\u002Fwww.amazon.com\u002FOptics-5th-Eugene-Hecht\u002Fdp\u002F0133977226?_encoding=UTF8&language=en_US&linkCode=ll1&linkId=d38230d12a814b81abb8a8b5201ebb99&qid=1618965492&ref_=as_li_ss_tl&sr=1-1&tag=susanfowler-20). The classic optics textbook.\n- **Particle Physics:** [Quarks and Leptons by Halzen and Martin](https:\u002F\u002Fwww.amazon.com\u002FQuarks-Leptons-Introductory-Particle-Physics\u002Fdp\u002F0471887412?dchild=1&keywords=martin%20particle%20physics&language=en_US&linkCode=ll1&linkId=6f72bd02a7aa2a2d8ecc89ebc34116f9&qid=1618981557&ref_=as_li_ss_tl&s=library&sr=1-5&tag=susanfowler-20). Wonderful overview that’s fun to read and work through. Supplement this with [Modern Particle Physics by Mark Thomson](https:\u002F\u002Fwww.amazon.com\u002FModern-Particle-Physics-Mark-Thomson\u002Fdp\u002F1107034264?dchild=1&keywords=particle%20physics&language=en_US&linkCode=ll1&linkId=1808f5c36867403219c827ea03e498ff&qid=1618982150&ref_=as_li_ss_tl&s=library&sr=1-5&tag=susanfowler-20), which is up-to-date on contemporary discoveries like the Higgs.\n- **Quantum Computing**:[Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang](https:\u002F\u002Fwww.amazon.com\u002FQuantum-Computation-Information-10th-Anniversary\u002Fdp\u002F1107002176?dchild=1&keywords=quantum%20computing&language=en_US&linkCode=ll1&linkId=6071735407ef7522e21c19395a51322e&qid=1618965299&ref_=as_li_ss_tl&s=library&sr=1-30&tag=susanfowler-20). Also known as “Mike and Ike,” this is _the_ standard introduction to quantum information and computation.\n- **Solid-State Physics:** [Solid-State Physics by Ashcroft and Mermin](https:\u002F\u002Fwww.amazon.com\u002FSolid-State-Physics-Neil-Ashcroft\u002Fdp\u002F8131500527?crid=2S8RO77XRYDXS&dchild=1&keywords=ashcroft%20and%20mermin%20solid%20state%20physics&language=en_US&linkCode=ll1&linkId=ed543039975467b23595195e55fcdaaf&qid=1618977068&ref_=as_li_ss_tl&sprefix=ashcroft%20and%20mer%2Cdigital-text%2C222&sr=8-1&tag=susanfowler-20). The classic introductory solid-state textbook. Supplement with [Introduction to Solid State Physics by Kittel](https:\u002F\u002Fwww.amazon.com\u002FIntroduction-Solid-Physics-Charles-Kittel\u002Fdp\u002F047141526X?crid=2ZLUATKWBISXC&dchild=1&keywords=kittel%20solid%20state%20physics&language=en_US&linkCode=ll1&linkId=9dc5ed44fcbf10f4ea8624a12feddbfc&qid=1619025990&ref_=as_li_ss_tl&s=library&sprefix=kittel%20%2Cstripibrary%2C227&sr=1-1&tag=susanfowler-20).\n- **String Theory:** [String Theory: Volume 1, An Introduction to the Bosonic String](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB00AKE1RLW?language=en_US&linkCode=ll1&linkId=f9dfb7bf40a0d71fa3fdd619c5ba240c&ref_=as_li_ss_tl&storeType=eibrary&tag=susanfowler-20) and [String Theory: Volume 2, Superstring Theory and Beyond](https:\u002F\u002Fwww.amazon.com\u002Fgp\u002Fproduct\u002FB00AKE1ROO?language=en_US&linkCode=ll1&linkId=bd5385577fe6167771edf2b3f216950b&ref_=as_li_ss_tl&storeType=eibrary&tag=susanfowler-20), by the late [Joe Polchinski](https:\u002F\u002Fwww.quantamagazine.org\u002Fjoe-polchinski-physicist-who-developed-deep-ideas-and-paradoxes-dies-at-63-20180220\u002F); and [String Theory and M-Theory: A Modern Introduction](https:\u002F\u002Fwww.amazon.com\u002FString-Theory-M-Theory-Modern-Introduction-ebook\u002Fdp\u002FB00AKE1SA2?language=en_US&linkCode=ll1&linkId=cf6cb87bcf439b832507b213cb1c3625&pd_rd_i=B00AKE1SA2&pd_rd_r=2f8b30eb-52e9-4d68-be57-85266802700e&pd_rd_w=nnUNY&pd_rd_wg=OznzN&pf_rd_p=78971f67-4c78-4f07-b5c1-ee9acd72068c&pf_rd_r=XSE51QVTY28WEJEM35GP&psc=1&ref_=as_li_ss_tl&tag=susanfowler-20). I found it really enjoyable to pair Polchinski’s library with Becker Becker Schwarz when I was learning string theory — they complement each other well.",[73,77,81,85,89,93,109],{"title":74,"url":75,"items":76},"پیشگفتار","#پیشگفتار",[],{"title":78,"url":79,"items":80},"فیزیک چیست؟ کلیدی برای درک جهان","#فیزیک-چیست-کلیدی-برای-درک-جهان",[],{"title":82,"url":83,"items":84},"مکانیک کلاسیک: حرکت اجسام، از پرتاب یک توپ تا مدار ماه.","#مکانیک-کلاسیک-حرکت-اجسام-از-پرتاب-یک-توپ-تا-مدار-ماه",[],{"title":86,"url":87,"items":88},"چالش‌های یادگیری فیزیک","#چالشهای-یادگیری-فیزیک",[],{"title":90,"url":91,"items":92},"معرفی دوره‌های سوزان ریگتی","#معرفی-دورههای-سوزان-ریگتی",[],{"title":94,"url":95,"items":96},"Before You Begin","#before-you-begin",[97,101,105],{"title":98,"url":99,"items":100},"undefinedPopular library on Physics","#popular-library-on-physics",[],{"title":102,"url":103,"items":104},"undefinedMathematical and Scientific Preliminaries","#mathematical-and-scientific-preliminaries",[],{"title":106,"url":107,"items":108},"undefinedHow to Study","#how-to-study",[],{"title":110,"url":111,"items":112},"undefinedUndergraduate Physics","#undergraduate-physics",[113,117,121,125,129,133,137,141,145,149,153,157,160,164,168,172,176,180,184],{"title":114,"url":115,"items":116},"undefinedOverview","#overview",[],{"title":118,"url":119,"items":120},"undefined1. 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