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What I need is to fill my gap of physics in quantum mechanics. I don't need too many explanation on why math is correct. I need explanations and exercises on physics. This is not a request for rigorous math nor is it a request for books that use math lingua.

My current background is good in classical mechanics (hamiltonian/lagrangian, & statistical stuff). My math background is very good in linear algebra (hilbert spaces, tensors, analysis, probability etc). I am also familiar with quantum computation & information stuff, basically qubits. I've also attended a few courses on quantum mechanics both in college and in youtube. The problem however is I still feel I missing some key concepts in Quantum mechanics and need a book that covers basic physics behind the math very well and has really good collection of exercises.

Pardon if this question is asked elsewhere or is off-topic.

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  • $\begingroup$ Albert Messiah (amazon.com/Quantum-Mechanics-2-Volumes-1/dp/0486409244) is pretty mathematical, in my opinion, addressing most of the problems to their mathematical behaviour. $\endgroup$ – gented Oct 5 '15 at 16:38
  • $\begingroup$ You may be interested in L. A. Takhtajan's Quantum mechanics for Mathematicians (American Mathematical Society, 2008) and L. D. Faddeev and O. A. Yakubovskii's Lectures on quantum mechanics for mathematics students (American Mathematical Society, 2009). They tend to go more for in-depth derivations and mathematical results than for simple insights about key concepts, though. $\endgroup$ – Emilio Pisanty Oct 5 '15 at 16:56
  • $\begingroup$ Also the fairly new book by Hall, quantum theory for mathematicians. $\endgroup$ – yuggib Oct 5 '15 at 17:05
  • $\begingroup$ Related: physics.stackexchange.com/q/22409/2451 , physics.stackexchange.com/q/44102/2451 , and links therein. $\endgroup$ – Qmechanic♦ Oct 5 '15 at 17:05
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    $\begingroup$ You should be careful how you word your request. Often when mathematicians say they want a physics book "for mathematicians," they mean "without all that unrigorous intuition or any of those pesky examples or applications," whereas you want a book "for people who know the math." This might be hard to find, since most books with "more physics and less maths" are like that because they assume the reader doesn't know any math at all. $\endgroup$ – user10851 Oct 5 '15 at 18:33
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There's a book by Sudbery called "Quantum Mechanics and the Particles of Nature", subtitled "An Outline for Mathematicians". This would seem to be just what you're looking for.

I'd also highly recommend Dirac's Principles of Quantum Mechanics. The math isn't always completely rigorous, but he thinks like a mathematician. At the same time, he frequently takes the trouble to explain the motivation and why (in retrospect) the constructions he's making have got to be the right ones.

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    $\begingroup$ Dirac's Principles of Quantum Mechanics would be the ideal book for the OP, were it not for the fact that there are no exercises in the book. Still, I do think the OP should read this book and then supplement that with another book containing a lot of exercises. $\endgroup$ – Count Iblis Oct 5 '15 at 19:53
  • $\begingroup$ Tempted to try out Dirac's book. Will wait for a few more days before I decide. Thanks. $\endgroup$ – Anita Oct 6 '15 at 16:48
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I think the best book ever written on QM which makes the fundamentals crystal clear with a full mathematical consistency is Modern Quantum Mechanics by J. J. Sakurai. If you master this book than finding notational mistakes and even logical errors on anything written about QM becomes like eating popcorn while watching a Bruce Willis movie.

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