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moyal evolution operator

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3 - The Phase Space Formulation of Quantum Mechanics
Marcos Mariño, Université de Genève
Book:

Advanced Topics in Quantum Mechanics

Published online:

02 December 2021

Print publication:

09 December 2021, pp 114-158
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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.