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
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).