Nonpointlike Particles in Harmonic Oscillators

TL;DR

This paper investigates how modifications to quantum mechanics that imply particles are nonpointlike affect the energy levels of particles in harmonic oscillators, revealing degeneracy removal and finite localization bounds.

Contribution

It provides a perturbative calculation of energy level corrections for nonpointlike particles in harmonic oscillators, highlighting the impact of modified commutation relations.

Findings

Degeneracy of energy levels is generally removed.

Finite lower bounds to spatial localization are induced.

Perturbative energy corrections are computed for nonpointlike particles.

Abstract

Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty $\Delta x$ can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation relations induce a finite lower bound to spatial localisation. Here, we perturbatively calculate the corrections to the energy levels of an in this sense nonpointlike particle in isotropic harmonic oscillators. Apart from a special case the degeneracy of the energy levels is removed.