Harmonic oscillator in an elastic medium with a spiral dislocation

TL;DR

This paper analytically solves the Schrödinger equation for a 2D harmonic oscillator in an elastic medium with a spiral dislocation, exploring topological effects on quantum confinement and potential Aharonov-Bohm phenomena.

Contribution

It provides an exact solution for the harmonic oscillator in a medium with a spiral dislocation and analyzes the topological effects on quantum states.

Findings

Analytical solutions for the Schrödinger equation with spiral dislocation

Identification of topological effects on quantum confinement

Discussion of possible Aharonov-Bohm-type effects

Abstract

We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schr\"odinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.