| 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. That being said let's start with the maths you will need to be comfortable with: - Complex Numbers (e^(i*theta)) - Linear Algebra (Matrix Multiplication, Basis of a vector space, Finding Eigenvalues) - Calculus and some Differential Equations (Taylor Expansions, Solving DEs) - Probability, Expectation values and Distributions 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): - Analysis (My math major friends say that functional analysis is required later on) - Hamiltonian Mechanics (QM is littered with Hamiltonians) - Group theory (if you want to get into Particle Physics) 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: - The Feynman Lectures on Physics, Volume I available at https://feynmanlectures.caltech.edu/I_toc.html - Structure and Interpretation of Classical Mechanics by Sussman and Wisdom available at https://mitpress-request.mit.edu/sites/default/files/titles/... As for books, at uni we used: - Quantum Mechanics by McIntyre, Manogue and Tate during 2nd year - A Modern Approach to Quantum Mechanics by Townsend during 3rd year They generally do a good job covering the material and explain things well. As for other resources, I haven't read these but they are generally recommended: - Introduction to Quantum Mechanics by David Griffiths (I liked the author's writing style in his EM book) - The Feynman Lectures on Physics, Volume III available at https://feynmanlectures.caltech.edu/III_toc.html - Quantum Computing Since Democritus by Scott Aaronson (I was recommended this for understanding why complex numbers are used in QM) Some other miscellaneous resources: - http://www.staff.science.uu.nl/~gadda001/goodtheorist/primar... - https://www.youtube.com/3blue1brown (The essence of Linear Algebra series is excellent) - https://ocw.mit.edu/index.htm (In case you want to watch lectures) - https://physicstravelguide.com/ 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. Let me know if you have any further questions. QM is damn cool dude, I hope you have a fun time delving into it. |