Quantum mechanics
Introductory to intermediate
Shankar, Principles of Quantum mechanics
Sakurai, Modern quantum mechanics
Messiah, Quantum mechanics, vols 1 & 2
Schwabl, Advanced quantum mechanics
Weinberg, Lectures on quantum mechanics
Jackson, Mathematics for quantum mechanics
Gustafson and Sigal, Mathematical concepts of quantum mechanics
Advanced and special topics
Tannoudji et al, Quantum mechanics, vols 1--3
Marino, Advanced topics in quantum mechanics
Sternberg, A mathematical companion to quantum mechanics
Prugovecki, Quantum mechanics in Hilbert space
Moretti, Spectral theory and quantum mechanics
Mackey, Mathematical foundations of quantum mechanics
Strocchi, An introduction to the mathematical structure of quantum mechanics
Faddeev and Yakubovskii, Lectures on quantum mechanics for mathematics students
Takhtajan, Quantum mechanics for mathematicians
Hall, Quantum theory for mathematicians
Glimm and Jaffe: Quantum physics: a functional integral point of view
"Quantum chaos" and related
Gutzwiller, Chaos in classical and quantum mechanics
Stockmann, Quantum chaos: an introduction
Wimberger, Nonlinear dynamics and quantum chaos
Haake, Gnutzmann and Kus, Quantum signatures of chaos
Casati and Chirikov (eds), Quantum Chaos: Between Order and Disorder
Mehta, Random matrices
Deift and Gioev, Random matrix theory
Tao, Topics in random matrix theory
Akemann et al, The Oxford handbook of random matrix theory
Quantum information
Wilde, Quantum information theory
Watrous, The theory of quantum information
Hayashi, Quantum information theory: mathematical foundation
Ohya and Volovich, Mathematical foundations of quantum information and computation and its applications
Mermin, Quantum computer science: an introduction
Scherer, Mathematics of quantum computing: an introduction
Gruska, Quantum computing
Portugal, Quantum Walks and Search Algorithms
Categories for Quantum Theory: An Introduction
Quantum cryptography
Wolf: Quantum key distribution: an introduction
Relevant mathematics:
- Basic functional analysis
- operator theory
- linear PDEs
- some measure and probability theory
- basic distribution theory
- C* algebras
- von Neumann algebras
- representation theory of Lie groups (including finite and countable groups).