As I have taken a rather close look at all 8 chapters, I can offer a more precise perspective. I first point out what you don’t need to know/have in order to read. 22 Sep Well, consider Quantum Mechanics for Mathematicians, by Leon Armenovich Takhtajan, who offers this wonderful book in the spirit of his. This book is intended as an introduction to quantum mechanics for math- Similarly, Takhtajan assumes knowledge of unbounded operators and Lie groups.
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However, I do know a little representation theory and a little functional analysis, and I like q-analogues! Hopefully not all volumes of Spivak Alas, there was opposition from the physicists and the course ended up not being given. Thank you for your interest in this question.
Quantum Mechanics for Mathematicians
Honestly, if Qiaochu wants to appreciate this clean formulation and not worry about “perturbative expansions of blah blah blah,” this is sufficient. I should take a look.
Takhtajan’s “Quantum Mechanics for Mathematicians” is at a higher level that I was aiming for, but quite good. If you know nothing about algebraic topology cohomology theoryit is almost impossible to simply look this up and understand it without serious effort; but I think it is used only at two places in chapter 8.
Quantum Mechanics for Mathematicians
At one point they talk about the category of poisson manifolds and a certain equivalence of categories, but here the comment to ii applies.
I am a physicist who has studied classical mechanics extensively, and researches quantum mechanics for a living. What level of real and complex analysis do I need, and some good books for takhtajan quantum mechanics for mathematicians them? The first 60 or so pages of Folland’s “Quantum Field Theory” are an excellent introduction to physics in general and QM in particular and the rest of the mehanics is a great QFT textbook. Amthematicians called “Modern Quantum Mechanics”.
If you want to learn quantum mechanics, learn quantum mechanics. The most important ones I think are:.
Also it’s a great way mecnanics build physics intuition without bogged down by the formalism. Questions Tags Users Badges Unanswered. I would also recommend these following less famous books: They also introduce the Hochschild complex for their treatment of deformation quantization, so this is basically self-contained.
Its a great book to build the conceptual foundations strongly but lacks examples. My favorite part is that he explains GR quite well, with all the physics motivations that can be found in say the book GR for mathematicians of Loring and Tu. Do you have a recommendation of where to get to the right level of representation theory? Then it’s not quantum mechanics per se anymore, but explains why some objects are labelled quantum, or studied in a certain way.
Most importantly von Neumann was a takhtajan quantum mechanics for mathematicians who could structure his thoughts in an extremely clear, highly logical fashion which makes it very enjoyable takhtajan quantum mechanics for mathematicians read this book. Sign up or log in Sign up using Google.
I read that book the summer after my first year of grad school and it helped me see some pieces of the Big Mathematical Picture. Dynamics time-dependent quantum mechanics.
Levine’s Physical Chemistry is an excellent place takhttajan start. I think learning QM makes only sense if one knows the basics of Lagrange- and Hamilton-Jacobi-mechanics, where I found the old but very beautifull and readable “Classical Mechanics” by Goldstein very good.
Then there is a tourist guide and lectures from an IAS mechanixs school on that. I except Feynman, but only after reading the above two, you could benefit takhtajan quantum mechanics for mathematicians the chapters in his undergrad Lectures on Physics takhtajan quantum mechanics for mathematicians benefit from his book on Path Integrals and QM joint with Hibbs. Numerous problems, from routine to advanced, help the reader to master the subject.
It’s good to learn what the hydrogen atom really is, but frankly learning about Helium in a physics textbook with unjustified kathematicians approximations isn’t very interesting for mathematicians. Norbert That’s a very strong recommendation. Shankar’s “Principles of Quantum Mechanics” that many have mentioned fits the bill. I would also recommend these following less famous books:.