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. (1) Classical mechanics: Principle of the least action. Lagrangian  L. A. Takhtajan, Quantum Mechanics for Mathematicians, American Mathematical. Society.
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An understanding of Borel sets An understanding of manifolds of all kinds so a solid Differential Geometry text Should know transforms besides Laplace and Fourier I, also, visited his course website at Stony Brook University and this is what I found. I would especially recommend it for people who study mathematics since it’s written from this point of view and not in the sometimes strange physicists language aka no bra-ket notation, no inexact use of mathematical facts etc. In my opinion Feynman’s Lectures in Physics is great for insight, but it’s a terrible idea to learn anything from it the first time – remember that when Feynman actually lectured, most of the freshmen and sophomores the intended audience dropped the mechanivs, and were replaced by senior students!
I want to know the math that is required to read Takhtajan’s “Quantum Mechanics for Mathematicians”. Quantum Mechanics for Mathematicians This book is, in a sense, a continuation of the book by L. This list comes from Takhtajan recommendation of courses needed for the class:. Griffiths, Introduction to Quantum Mechanics, but keep in mind that it is aimed at physics or engineering students.
Review: Quantum Mechanics for Mathematicians | EMS
They also sometimes use very elementary fourier analysis, such as the plancherel theorem. Alas, there was opposition from the physicists and the course ended up not being given. Also, I don’t think it would be the best idea for the OP to try to learn the material ahead of time, but rather they should look it up as needed. So you are absolutely right in wanting to study Quantum Mechanics: Then it’s not quantum mechanics per se anymore, but explains why some objects are labelled quantum, or studied in a certain way.
The trickiest part of Quantum Theory is to get grips on the theory of angular momentum and spherical harmonics and Wigner’s D-matrices. I cannot recommend Tannor’s Introduction to Quantum Mechanics: You want to learn how physicists think and how they use this stuff to come up with real physical predictions. Numerous problems, from routine to advanced, help the reader to master the subject.
Norbert That’s a very strong recommendation.
Quantum Mechanics for Mathematicians
A book on quantum theory from someone who had an enormous impact on the subject, it’s very clear and quantum mechanics is cleanly developed and motivated from scratch. Shankar explains concepts well, and there is a large focus on examples. A Time-dependent Perspective enough as a really fantastic resource for learning how practicing physicists and chemists actually do these calculations, beyond the really simplistic calculations presented in most introductory texts. This is mentioned in the preface.
I’m very surprised only one person has mentioned Dirac’s Principles of Quantum Mechanics. At this level quantum mechanics is an application of linear algebra, so well suited for mathematics students. Is it necessary that I understand what a Hamiltonian is first? The normal route follows the historical one up to the s skipping too physical considerations for youand this is indeed done well in Takhtajan’s book chapters 1 to 5.
atical physics – Where does a math person go to learn quantum mechanics? – MathOverflow
Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. The quantum information community has really made abstract quantum theory interesting in the last 20 years or so. What level of real and complex analysis do I need, and some good books for learning them?
At least he doesn’t require complete understanding of the proofs of Fermat’s last theorem and the abc conjecture. I think there are some excellent recommendations above.
I Differential geometry generalities such as e. 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.
However, if you want to solve publishable problems then head towards quantum information: Its a great book to build the conceptual foundations strongly but lacks examples.
Post as a guest Name. The most important ones I think are: It’s not a hard-core pure math axiomatic approach to QM. I realize this is unrelated to nechanics question at hand, but does anyone know if there is a math equivalent to ‘t Hooft’s page that Scott links to here?
Are there any book at this level without any mistake? Dynamics time-dependent quantum mechanics. These days Brian C.
But you are very encouraging. You can safely ignore the paragraphs in the beginning about his page being only for people who want to win the Nobel prize in physics.
Yeah, it’s very mathematical, and it gets to SUSY a bit. Mathematjcians it does make me curious: