Supersymmetric variational energies of 3d confined potentials

TL;DR

This paper introduces a supersymmetric quantum mechanics-based variational method to compute energies of three-dimensional confined potentials, demonstrated on harmonic oscillator and Hulthén potentials, with results compared to existing methods.

Contribution

It proposes a general recipe for constructing superpotentials for 3D confined potentials within supersymmetric quantum mechanics.

Findings

Accurate energy estimates for 3D confined harmonic oscillator.

Effective approximation for the Hulthén potential energies.

Comparison shows good agreement with existing numerical results.

Abstract

Within the approach of Supersymmetric Quantum Mechanics associated with the variational method a recipe to construct the superpotential of three dimensional confined potentials in general is proposed. To illustrate the construction, the energies of the Harmonic Oscillator and the Hulth\'en potential, both confined in three dimensions are evaluated. Comparison with the corresponding results of other approximative and exact numerical results is presented.