Supersymmetric quantum mechanics, the variational method and a new shape invariant potential

TL;DR

This paper reviews how the variational method integrates with supersymmetric quantum mechanics to approximate energy spectra of non-solvable potentials and introduces a new exactly shape invariant potential.

Contribution

It combines the variational method with supersymmetric quantum mechanics and proposes a new exactly shape invariant potential.

Findings

Approximate energy spectra for Hulthen, Morse, and screened Coulomb potentials are obtained.

The method effectively bridges variational techniques with supersymmetric quantum mechanics.

A new exactly shape invariant potential is introduced.

Abstract

The association of the variational method with supersymmetric quantum mechanics through an ansatz for the superpotential is reviewed and the approximate energy spectra of non-exactly solvable potentials, such like the Hulthen, the Morse and the screened Coulomb potentials, in 3 dimensions, are presented. A sketch of a new exactly shape invariant potential is also presented.