Trapping of a particle in a short-range harmonic potential well

TL;DR

This paper investigates the eigenstates of a particle confined in a localized harmonic potential well, analyzing how changes in potential parameters affect these states and exploring asymptotic expansion results.

Contribution

It provides a detailed analysis of eigenstates in a short-range harmonic potential well, including effects of parameter variation and asymptotic behaviors.

Findings

Eigenstates depend sensitively on potential parameters.

Asymptotic expansions offer insights into eigenstate behavior.

Potential parameter variations significantly influence particle confinement.

Abstract

Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.