Remarks on the harmonic oscillator with a minimal position uncertainty

TL;DR

This paper explores a harmonic oscillator model with minimal position uncertainty, revealing its mathematical equivalence to a known quantum potential but highlighting differences in parameter choices that affect the physical spectrum interpretation.

Contribution

It demonstrates the equivalence of the minimal uncertainty harmonic oscillator to a known quantum potential and discusses how parameter choices influence the physical spectrum.

Findings

Mathematical equivalence to a known quantum potential

Parameter choice affects spectrum interpretation

Subtle differences alter physical discussion

Abstract

We show that this problem gives rise to the same differential equation of a well known potential of ordinary quantum mechanics. However there is a subtle difference in the choice of the parameters of the hypergeometric function solving the differential equation which changes the physical discussion of the spectrum.