The Wigner function negative value domains and energy function poles of the harmonic oscillator

TL;DR

This paper investigates the relationship between negative regions of the Wigner function and the poles of the energy function in a quantum harmonic oscillator, providing explicit expressions for energy distribution.

Contribution

It introduces an explicit expression for the energy distribution as a coordinate function and links Wigner function negativity to energy function poles.

Findings

Negative Wigner function domains correspond to energy function poles.

Explicit energy distribution expression derived for the quantum harmonic oscillator.

Identifies the connection between Wigner negativity and system singularities.

Abstract

For a quantum harmonic oscillator an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is shown for the quantum system in domains where the Wigner function has negative values.