Minimal Length and Bouncing Particle Spectrum

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.