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.
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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.
by Max Lein - arXiv
This text is aimed at graduate students in physics in mathematics and designed to give a comprehensive introduction to Weyl quantization and semiclassics via Egorov's theorem. An application of Weyl calculus to Born-Oppenheimer systems is discussed.
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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 Jan Govaerts - arXiv
A basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract algebraic aspects of quantization.