Bound states for the quantum dipole moment in two dimensions

TL;DR

This paper computes precise eigenvalues and eigenfunctions for a 2D quantum dipole, demonstrating an efficient variational method that improves upon previous approaches, with applications to dislocation studies.

Contribution

It introduces a more efficient Rayleigh-Ritz variational method using Slater-type functions for the 2D quantum dipole eigenproblem.

Findings

The variational method outperforms previous basis sets in efficiency.

Accurate eigenvalues and eigenfunctions are obtained for the 2D quantum dipole.

The model aids in understanding elastic effects of edge dislocations.

Abstract

We calculate accurate eigenvalues and eigenfunctions of the Schr\"odinger equation for a two-dimensional quantum dipole. This model proved useful for the study of elastic effects of a single edge dislocation. We show that the Rayleigh-Ritz variational method with a basis set of Slater-type functions is considerably more efficient than the same approach with the basis set of point-spectrum eigenfunctions of the two-dimensional hydrogen atom used in earlier calculations.