Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space

TL;DR

This paper calculates how generalized uncertainty principles (GUPs) modify the Wigner functions of a harmonic oscillator, highlighting potential observable effects in experiments.

Contribution

It provides a detailed analysis of GUP-induced corrections to the phase space representation of the harmonic oscillator, a novel extension in quantum mechanics.

Findings

GUP corrections significantly alter Wigner functions

Potential for experimental detection of GUP effects

Enhanced understanding of quantum phase space under GUP

Abstract

We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.