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3 - The Phase Space Formulation of Quantum Mechanics

Published online by Cambridge University Press:  02 December 2021

Marcos Mariño
Marcos Mariño
Affiliation:
Université de Genève
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Summary

This chapter presents Wigner’s approach to quantum mechanics, based on the Wigner function in phase space. It explains Wigner–Weyl quantization, which makes it possible to associate functions on phase space to wave functions and operators, and it develops the technology to do quantum mechanics in this formalism. This includes the star product, Moyal evolution,and star-eigenvalue equations. It also develops semiclassical methods in this formulation, and it has a section on Berry’s semiclassical formula for the Wigner function in one-dimensional systems.

Keywords

Wigner–Weyl quantizationstar productphase spaceMoyal evolution operatorsemiclassical methods in quantum mechanicsWigner functionHusimi distribution
Type
Chapter
Information
Advanced Topics in Quantum Mechanics , pp. 114 - 158
Publisher: Cambridge University Press
Print publication year: 2021

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