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. In addi- tion, physics books on quantum mechanics assume knowledge of classical example, Takhtajan begins with Lagrangian and Hamiltonian mechanics. 22 Sep Well, consider Quantum Mechanics for Mathematicians, by Leon Armenovich Takhtajan, who offers this wonderful book in the spirit of his.
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By a clever selection of the material and the clear way of exposing it, the book is recommended for graduate students in mathematics looking for applications in physics, as well as for student in physics desiring to be acquainted, in a rigorous but, at the same time, quick and accessible mecanics, with the basic mathematical tools used in quantum mathematics. One can, in fact, learn the foundations of QM without knowing Classical Mechanics at all, and I recommend reading the first six chapters of Dirac, The principles of quantum mechanics fro, to get a feeling for the physical concepts.
It does not assume any background in physics, but it is quite heavy on the math side it is used in a third year course in QM for mathematicians at the SNS of Pisa. Math packaged as “physics” sounds alright to me! The most important ones I think are:. You don’t need much physics background to learn to do basic calculations with wave functions, and to pick mechanicx ideas like observables-as-differential-operators.
VI A bit of general topology: Unfortunately, my physics background is a little lacking. I think there are some excellent recommendations above.
It’s not about lack of rigor, it’s dealing with non-solvable systems e. Riemannian Geometryby Peter Petersen, Springer, He includes a brief overview of classical mechanics from the symplectic POV, rendering moot much of the discussion below on whether or not one should learn CM first. Now there are at multiple papers on the quant-ph arXiv every day that do just that. I would guess Feynman is a good place mathematiicians learn QM, but it is clearly out-of-date in that it predates the exciting new field of quantum information science.
A Time-dependent Tkhtajan enough as a really fantastic resource for mahhematicians how practicing physicists and chemists actually do these calculations, beyond the really simplistic calculations presented in most introductory texts.
This is really where some of the strangest predictions of quantum mechanics come from, like the Qquantum paradox and spin statistics. Libraries and resellers, please contact cust-serv ams.
Quantum Mechanics for Mathematicians Share this page. I recommend against Shankar, he is not conceptually very careful.
atical physics – Where does a math person go to learn quantum mechanics? – MathOverflow
I like it better than the physics-y books Sakurai, etc. You’re in better shape knowing linear algebra well and not knowing any physics than you would be the other way around. If you are reading QM for “culture”, as I gather takhtajann are, the books which work well as intro texts for professionals are really irrelevant, so forget Sakurai, Gottfried, Landau, et hoc genus omne. Reed and Simon’s “Methods of Mathematical Physics” books are a must if you want to go in that direction.
I hope this is “of interest to mathematicians. I realize this is unrelated to the question at hand, but does anyone know if there is a math equivalent to ‘t Hooft’s page that Scott links to here? For a good introduction requiring minimal background you could try D.
Therefore exploring offline resources in this case could be especially fruitful. I recommend against Mackey or von Neumann, they have no physical insight, Varadarajan is even worse.
You shouldn’t have much trouble later figuring out how to translate the physics back into math.
You don’t have to take mechanics first, just linear algebra. After that it may be usefull to look into Hatfield’s “Quantum Field theory of point particles and strings” which Witten recommends.
Physical chemistry and materials science textbooks. This is one of the most beautiful facts I have ever learned. When I was in college, the books I was taught from were Sakurai’s “Modern quantum mechanics” and Townsend’s “A modern approach to quantum mechanics”.
The only things I know there is that “identities” and “Apostol” were misspelled. Dynamics time-dependent quantum mechanics. I agree with Scott firmly here. Online Price 1 Label: Post as a guest Name. Then there is a tourist guide and lectures from an IAS summer school on that. Otherwise, you’re just learning math packaged as “physics”. It doesn’t stress the physical intuition very much, but I learned a lot of basic quantum from the first chapter of Nielsen and Chuang.
Quantum Mechanics for Mathematicians
If you want to learn quantum mechanics, learn quantum mechanics. My undergraduate advisor said something very interesting to me the other day; it was something like mxthematicians knowing quantum mechanics is like never having heard a symphony.
To sum up and structure what others have said and add my grain of salt: If what you’re interested in is quantum field theory from a mathematical point of view, I’d suggest Folland’s recent book “Quantum field theory”.
I also think it would be a mistake to start with an overly mathematically-oriented QM course.