Wigner function under changes of reference frames

TL;DR

This paper studies how the Wigner function transforms when changing reference frames, deriving an integral formula for the transformation and illustrating it with basic examples.

Contribution

It introduces a new integral representation for the transformed Wigner function under reference frame changes, expanding understanding of phase space transformations.

Findings

Derived an integral transformation law for the Wigner function

Provided examples demonstrating the transformation process

Enhanced theoretical understanding of phase space in quantum mechanics

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.