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

TL;DR

This paper derives an explicit expression for the energy distribution of a polynomial oscillator and investigates the relationship between Wigner function negativity and energy function poles.

Contribution

It provides a new explicit formula for energy distribution and links Wigner function negativity to energy function poles in polynomial oscillators.

Findings

Energy distribution expressed explicitly in terms of coordinate and momentum.

Wigner function negativity correlates with the presence of energy function poles.

Identification of domains where the Wigner function is negative.

Abstract

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