Classical and quantum quasi-free position dependent mass; P\"oschl-Teller and ordering-ambiguity

TL;DR

This paper explores how classical-quantum correspondence influences the choice of ordering-ambiguity parameters in quantum mechanics with position-dependent mass, using the P"oschl-Teller model as a reference.

Contribution

It introduces a method to determine ordering-ambiguity parameters based on classical-quantum correspondence in position-dependent mass systems.

Findings

Classical-quantum correspondence constrains ambiguity parameters

Effective P"oschl-Teller model validates parameter choices

Position-dependent mass models are analyzed for consistency

Abstract

We argue that the classical and quantum mechanical correspondence may play a basic role in the fixation of the ordering-ambiguity parameters. We use quasi-free position-dependent masses in the classical and quantum frameworks. The effective P\"oschl-Teller model is used as a manifested reference potential to elaborate on the reliability of the ordering-ambiguity parameters available in the literature.