Harmonic oscillator with minimal length, minimal momentum, and maximal momentum uncertainties in SUSYQM framework

TL;DR

This paper derives exact harmonic oscillator energy levels within a GUP framework predicting maximal and minimal uncertainties, using SUSYQM methods and exploring effects of an electric field.

Contribution

It introduces a novel application of SUSYQM to a GUP model with maximal and minimal uncertainties, deriving exact spectra and partner Hamiltonians.

Findings

Exact eigenvalues for the harmonic oscillator in GUP with maximal/minimal uncertainties.

Identification of a hierarchy of partner Hamiltonians with shifted parameters.

Analysis of electric field effects on the energy spectrum.

Abstract

We consider a Generalized Uncertainty Principle (GUP) framework which predicts a maximal uncertainty in momentum and minimal uncertainties both in position and momentum. We apply supersymmetric quantum mechanics method and the shape invariance condition to obtain the exact harmonic oscillator eigenvalues in this GUP context. We find the supersymmetric partner Hamiltonians and show that the harmonic oscillator belongs to a hierarchy of Hamiltonians with a shift in momentum representation and different masses and frequencies. We also study the effect of a uniform electric field on the harmonic oscillator energy spectrum in this setup.