Minimal Length and Bouncing Particle Spectrum

TL;DR

This paper investigates how the Generalized Uncertainty Principle modifies the energy spectrum and wave functions of a quantum bouncing particle, providing insights into quantum gravity effects in a simple gravitational system.

Contribution

It introduces a calculation of energy levels and wave functions for a quantum bouncer incorporating GUP, extending traditional quantum mechanics results.

Findings

GUP alters the energy spectrum of the quantum bouncer

Wave functions are modified by the GUP parameter

Potential experimental applications are discussed

Abstract

In this paper we study the effects of the Generalized Uncertainty Principle (GUP) on the spectrum of a particle that is bouncing vertically and elastically on a smooth reflecting floor in the Earth's gravitational field (a quantum bouncer). We calculate energy levels and corresponding wave functions of this system in terms of the GUP parameter. We compare the outcomes of our study with the results obtained from elementary quantum mechanics. A potential application of the present study is discussed finally.