Let's say that you have a basic understanding of college level Mathematics and Physics. And you would like to start learning Quantam Physics. You are not looking for short cuts. You are ready to put in years, basically learning in the hard way.<p>What would be the first steps?
I'm not sure what's college level physics like, but for me (math/CS background) learning quantum physics was:<p>- Quantum algorithms and computing: "Quantum Computing Since Democritus" by Scott Aaronson [0] and "Quantum Computation and Quantum Information" by Nielsen and Chuang [1]. "Quantum Computer Science" by Mermin is really good too.<p>- Leonard Susskind's lectures on quantum mechanics [3]<p>- "Introduction to Quantum Mechanics" by David Griffiths [4] -- just your regular QM textbook. Recommended by many and I found the explanations clear and easy to follow<p>- also there are some recommendations by John Baez [5], that I've personally not checked out, but when Baez recommends something, it's good!<p>Note that I'm not a physicist and doing it only for fun, so would be interesting to hear from people with proper physics education!<p>[0] <a href="https://www.scottaaronson.com/democritus/" rel="nofollow">https://www.scottaaronson.com/democritus/</a><p>[1] <a href="https://en.wikipedia.org/wiki/Quantum_Computation_and_Quantum_Information" rel="nofollow">https://en.wikipedia.org/wiki/Quantum_Computation_and_Quantu...</a><p>[2] <a href="https://www.cambridge.org/core/books/quantum-computer-science/66462590D10C8010017CF1D7C45708D7" rel="nofollow">https://www.cambridge.org/core/books/quantum-computer-scienc...</a><p>[3] <a href="https://theoreticalminimum.com/courses/quantum-mechanics/2012/winter" rel="nofollow">https://theoreticalminimum.com/courses/quantum-mechanics/201...</a><p>[4] <a href="https://physicspages.com/Griffiths%20QM.html" rel="nofollow">https://physicspages.com/Griffiths%20QM.html</a><p>[5] <a href="http://math.ucr.edu/home/baez/books.html#quantum_mechanics" rel="nofollow">http://math.ucr.edu/home/baez/books.html#quantum_mechanics</a>
Generically, I would work through Griffiths first, and then Shankar and/or Sakurai.<p>You can probably refine it a little bit based on your motivation to learning quantum physics, and what level of mastery you need.
For context I studied physics for about 2 years in university, before I switched to maths with the intention of returning with better mathematical foundations.<p>That being said let's start with the maths you will need to be comfortable with:<p>- Complex Numbers (e^(i*theta))<p>- Linear Algebra (Matrix Multiplication, Basis of a vector space, Finding Eigenvalues)<p>- Calculus and some Differential Equations (Taylor Expansions, Solving DEs)<p>- Probability, Expectation values and Distributions<p>That's probably what you'll need to dive into textbooks. For a deeper understanding, it would help to know these (worry about these later):<p>- Analysis (My math major friends say that functional analysis is required later on)<p>- Hamiltonian Mechanics (QM is littered with Hamiltonians)<p>- Group theory (if you want to get into Particle Physics)<p>I'd also recommend having a good grasp on classical mechanics because quantum mechanics builds on it. On my todo list is to review this using:<p>- The Feynman Lectures on Physics, Volume I available at <a href="https://feynmanlectures.caltech.edu/I_toc.html" rel="nofollow">https://feynmanlectures.caltech.edu/I_toc.html</a><p>- Structure and Interpretation of Classical Mechanics by Sussman and Wisdom available at <a href="https://mitpress-request.mit.edu/sites/default/files/titles/content/sicm/book.html" rel="nofollow">https://mitpress-request.mit.edu/sites/default/files/titles/...</a><p>As for books, at uni we used:<p>- Quantum Mechanics by McIntyre, Manogue and Tate during 2nd year<p>- A Modern Approach to Quantum Mechanics by Townsend during 3rd year<p>They generally do a good job covering the material and explain things well.<p>As for other resources, I haven't read these but they are generally recommended:<p>- Introduction to Quantum Mechanics by David Griffiths (I liked the author's writing style in his EM book)<p>- The Feynman Lectures on Physics, Volume III available at <a href="https://feynmanlectures.caltech.edu/III_toc.html" rel="nofollow">https://feynmanlectures.caltech.edu/III_toc.html</a><p>- Quantum Computing Since Democritus by Scott Aaronson (I was recommended this for understanding why complex numbers are used in QM)<p>Some other miscellaneous resources:<p>- <a href="http://www.staff.science.uu.nl/~gadda001/goodtheorist/primarymathematics.html" rel="nofollow">http://www.staff.science.uu.nl/~gadda001/goodtheorist/primar...</a><p>- <a href="https://www.youtube.com/3blue1brown" rel="nofollow">https://www.youtube.com/3blue1brown</a> (The essence of Linear Algebra series is excellent)<p>- <a href="https://ocw.mit.edu/index.htm" rel="nofollow">https://ocw.mit.edu/index.htm</a> (In case you want to watch lectures)<p>- <a href="https://physicstravelguide.com/" rel="nofollow">https://physicstravelguide.com/</a><p>All of this is at an undergraduate level. It's probably best to grab one of the books and start running through, consulting the others when you want another explanation.<p>Let me know if you have any further questions. QM is damn cool dude, I hope you have a fun time delving into it.