Quantum Mechanics Book for someone who know math 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.
 A: 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.  
A: A very good resource that treats a great number of physical topics assuming some degree of mathematical maturity is Gustafson and Sigal's Mathematical Concepts of Quantum Mechanics. Despite the title, the book isn't your typical rigorous resource aimed at mathematicians. I quote the following from the book's preface:

Given our time constraint, we have often pursued mathematical content
at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous.

This book clearly meets your needs as it requires some pre-requisite knowledge in mathematics (albeit very briefly reviewed if necessary) as mentioned in the preface, which i quote:

Prerequisites for this book are introductory real analysis (notions of vector space, scalar product, norm, convergence, Fourier transform) and complex analysis, the theory of Lebesgue integration, and elementary differential
equations. These topics are typically covered by the third year in mathematics
departments. The first and third topics are also familiar to physics undergraduates. However, even in dealing with mathematics students we have found it useful, if not necessary, to review these notions, as needed for the course. Hence, to make the book relatively self-contained, we briefly cover these subjects, with the exception of Lebesgue integration. Those unfamiliar with the latter can think about Lebesgue integrals as if they were Riemann integrals. This said, the pace of the book is not a leisurely one and requires, at least for beginners, some amount of work.

This book covers a vast variety of topics that are not found in your typical quantum mechanics textbook along with topics that usually are present as well. It would be prudent to use this book as a primary resource despite the slightly more difficult pace due to the clarity of exposition.
A: 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.
