An Introduction to Microlocal Analysis
by Richard B. Melrose, Gunther Uhlmann
Publisher: MIT 2008
Number of pages: 182
One of the origins of scattering theory is the study of quantum mechanical systems, generally involving potentials. The scattering theory for perturbations of the flat Laplacian is discussed with the initial approach being via the solution of the Cauchy problem for the corresponding perturbed wave equation.
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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.
by Peter Woit - Columbia University
These notes cover the basics of quantum mechanics, from a point of view emphasizing the role of unitary representations of Lie groups in the foundations of the subject. The approach to this material is simultaneously rather advanced...
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.
by Gianfausto Dell'Antonio - Sissa, Trieste
The theory which is presented here is Quantum Mechanics as formulated in its essential parts on one hand by de Broglie and Schroedinger and on the other by Born, Heisenberg and Jordan with important contributions by Dirac and Pauli.