A singular position-dependent mass particle in an infinite potential well

TL;DR

This paper investigates a unique quantum particle with a position-dependent mass in an infinite potential well, establishing a mathematical correspondence with a well-known Poschl-Teller potential and exploring ordering ambiguities.

Contribution

It introduces a novel approach to analyze a singular position-dependent mass particle, mapping its Hamiltonian to a Poschl-Teller type and proposing new ordering ambiguity parameters.

Findings

Established a Hamiltonian mapping to Poschl-Teller potential

Proposed new ordering ambiguity parameters

Provided explicit correspondence between Hamiltonians

Abstract

We consider an unusual singular position=dependent-mass particle in an infinite potential well. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian and a Poschl-Teller type reference Hamiltonian is obtained. New ordering ambiguity parametric setting are suggested.