Mathematical Concepts of Quantum Mechanics
by S. Gustafson, I.M. Sigal
Publisher: University of Toronto 2001
Number of pages: 185
These lectures cover a one term course taken by a mixed group of students specializing either in mathematics or physics. We decided to select material which illustrates an interplay of ideas from various fields of mathematics, such as operator theory, probability, differential equations, and differential geometry.
Home page url
Download or read it online for free here:
by Gerald Teschl - American Mathematical Society
This is a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required.
by Douglas Lundholm - arXiv.org
These are lecture notes for a master-level course given at KTH, Stockholm, in the spring of 2017, with the primary aim of proving the stability of matter from first principles using modern mathematical methods in many-body quantum mechanics.
by Leonid Polterovich - arXiv
We discuss a quantum counterpart of certain constraints on Poisson brackets coming from 'hard' symplectic geometry. They can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics.
by Ingemar Bengtsson - Stockholms universitet, Fysikum
These are the lecture notes from a graduate course in the geometry of quantum mechanics. The idea was to introduce the mathematics in its own right, but not to introduce anything that is not directly relevant to the subject.