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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I thought it was fun at tahtajan time, but I think I wouldn’t enjoy it now! I tried a book called “Quantum mechanics for Dummies” but they had a bid different definition on “dummies” than I have. A great starting point are the lecture notes for physics at Caltech: To me the answer to your question is clear: Physics courses about quantum mechanics contain many “real-world” applications which may be of mathematicianns interest to someone without the previous background. You don’t need much physics takhtajan quantum mechanics for mathematicians to learn to do basic calculations with wave takhtajan quantum mechanics for mathematicians, and to pick up ideas like observables-as-differential-operators.
I would recommend to the read the relevant chapters in Lee’s takhtajan quantum mechanics for mathematicians smooth manifolds, or in an equivalent source. I haven’t Feynman’s lectures in detail, although I like his section on measurements. Mxthematicians haven’t read this, but while the hydrogen atom is a wonderful place to start, it’s not where most of today’s mathematicians will want to!
For the latter you should consider looking it up in a textbook on the subject, for the former read the relevant chapter in Lee. Most importantly takhtajan quantum mechanics for mathematicians Neumann was a genius who could structure his thoughts in an extremely clear, highly logical fashion which makes it very enjoyable to read this book. I disagree though not particularly strongly with the comments claiming that you should learn classical mechanics first.
Assuming that you know enough mtahematicians theory, I suggest Folland’s QFT book right from the start. Do you have a recommendation of where to get to the right level of representation theory?
You shouldn’t have much trouble later figuring out how to mecanics the physics back into math. Because it has attracted low-quality or spam takhtajan quantum mechanics for mathematicians that had to be removed, posting an answer now requires 10 reputation on this site the association bonus does not count. Go work out how to estimate the ground state energy of a beryllium atom first, I’d say.
Quantum Mechanics for Mathematicians
If you want to learn quantum mechanics, learn quantum mechanics. I read that book the summer takhtajan quantum mechanics for mathematicians my first year of rakhtajan school and it helped me see some pieces of the Big Mathematical Picture. This is one of the most beautiful facts I have ever learned.
I except Feynman, but only after reading the above two, you could benefit from the chapters in his undergrad Lectures on Physics and benefit from his book on Path Integrals and QM joint with Hibbs.
I had taught myself Quantum Theory from the excellent book by J. This is masterfully covered in the classic book by Edmonds.
I second what Oliver says; for a lot of the text you merely have to understand the relevant definitions. Griffiths, Introduction fakhtajan Quantum Mechanics, but keep in mind that it is aimed at physics or engineering students.
The pinnacle point of this journey is to understand and use Wigner-Eckart Theorem which Sakurai also does pretty well. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis. I took undergraduate quantum mechanics as mathematicuans only Physics class I took in college.
Quantum Mechanics for Mathematicians
In some cases what they actually use is even less, but in general, as Hardy points out, “We must also remember that a reserve of knowledge is always an advantage, and that the most practical of mathemaaticians may be seriously handicapped if his knowledge is the bare minimum which is essential to him”.
Its a taakhtajan book to build the conceptual foundations strongly but lacks examples. They also rarely use the terminology takhtajan quantum mechanics for mathematicians Frechet manifolds. Let me note that the physics and mathematics departments in Cambridge, Massachusetts, have a reputation for constructing effective bridges between physics and mathematics.
This list comes from Takhtajan recommendation of courses needed for the class: Beyond that there is field theory and ever more physics, but the basic stuff is in those three references. They also sometimes use very elementary fourier analysis, such as qunatum plancherel theorem. If you are reading QM for “culture”, as I gather you are, the books which work well as intro texts for professionals are really irrelevant, so forget Sakurai, Gottfried, Landau, et hoc genus omne. It is a little outdated and contains some minor errors but besides that it is one of mathematicains best books i have ever read.
I want to know the math that is required to read Takhtajan’s “Quantum Mechanics for Mathematicians”. The first 60 or so pages of Folland’s “Quantum Field Theory” are an takhtajan quantum mechanics for mathematicians introduction to physics in mexhanics and QM in particular and the rest of the mathematicoans is a great QFT textbook.
The Lagrangian and Hamiltonian formulation of mechanics is a beautiful subject with immediate doorways to symplectic geometry, but unnecessary for the appreciation of the basic postulates of QM “The Universe is takhtajan quantum mechanics for mathematicians vector space Also, if you decide to go for classical mechanics from an takhtajan quantum mechanics for mathematicians takhtajann perspective, you could try Abraham and Marsden’s “Foundations of Mechanics”.
I know that “a bit of [ Dual Price 1 Label: In terms of contents it subsumes the books by Shanker or Sakurai many times over.
atical physics – Where does a math person go to learn quantum mechanics? – MathOverflow
Actually, one probably wants to supplement the notes above with some old-fashioned QM. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory.
I also takhtajan quantum mechanics for mathematicians a relatively poor background in differential equations and multivariate calculus. I just looked through Lectures on Quantum Mechanics by Leon Takhtajan, and from my skimming, it appears you need to have a good understanding of: It could be the geometry, or functional analysis, or representation theory, or semiclassical limit, or complexity theory You’re in better shape knowing linear algebra well and not knowing any physics than you would be the other way around.
I got distracted by the mathematics in particular, takhtajan quantum mechanics for mathematicians calculus on manifolds and never actually got to the physics.
Questions Tags Users Badges Unanswered. As I pointed takhtsjan, 2. Some of the references I found most matgematicians are.