The harmonic oscillator in a space with a screw dislocation

TL;DR

This paper calculates the energy levels of a harmonic oscillator in a space with a screw dislocation, revealing complex spectral features and demonstrating a variational method for accurate eigenvalues across different deformation parameters.

Contribution

It introduces a variational approach with a nonorthogonal basis to accurately determine eigenvalues of the harmonic oscillator in a space with screw dislocation, a novel setting.

Findings

Eigenvalues exhibit avoided crossings depending on the deformation parameter.

The variational method provides accurate results for a wide range of parameters.

The energy spectrum shows a rich structure influenced by the space deformation.

Abstract

We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of values of the space-deformation parameter. The energies exhibit a rich structure of avoided crossings in terms of such model parameter.