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arXiv:2411.09890

Wigner function under changes of reference frames

Jasel Berra–Montiel, G. F. Torres del Castillo

Published Nov 15, 2024• 0 citations
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Abstract

In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed Wigner function in both position and momentum representations. To illustrate our results, we include some basic examples.

DOI
10.48550/arxiv.2411.09890

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In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed Wigner function in both position and momentum representations. To illustrate our results, we include some basic examples.
We derive explicit expressions for the Wigner function of wave functions in DDD dimensions which depend on the hyperradius---that is, of sss waves. They are based either on the position or the momentum representation of the sss wave. The corresponding Wigner function depends on three variables: the absolute value of the DDD-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary sss wave and the energy eigenfunction of a free particle.