Nonsingular potentials from excited state factorization of a quantum system with position dependent mass

TL;DR

This paper introduces a modified factorization method for quantum systems with position-dependent mass, enabling the construction of non-singular isospectral Hamiltonians using excited state superpotentials.

Contribution

It presents a novel approach to eliminate singularities in position-dependent mass quantum systems through excited state factorization.

Findings

Successfully constructs non-singular isospectral Hamiltonians

Demonstrates the method with illustrative examples

Provides a new tool for quantum system analysis

Abstract

The modified factorization technique of a quantum system characterized by position-dependent mass Hamiltonian is presented. It has been shown that the singular superpotential defined in terms of a mass function and a excited state wave function of a given position-dependent mass Hamiltonian can be used to construct non-singular isospectral Hamiltonians. The method has been illustrated with the help of a few examples.