A quasi-free position-dependent-mass jump and self-scattering correspondence

TL;DR

This paper investigates quantum scattering effects of a particle with a position-dependent mass jump, revealing new insights into reflection and transmission phenomena and proposing a novel set of ordering ambiguity parameters.

Contribution

It introduces a new approach to analyze position-dependent mass jumps and identifies a unique set of ambiguity parameters within this framework.

Findings

Derived explicit reflection and transmission coefficients.

Identified a feasible set of ordering ambiguity parameters.

Linked mass jump effects to Dirac delta dipole interactions.

Abstract

A quasi-free quantum particle endowed with Heaviside position dependent mass jump is observed to experience scattering effects manifested by its by-product introduction of the derivative of the Dirac's-delta point dipole interaction. Using proper parametric mappings, the reflection and transmission coefficients are obtained. A new ordering ambiguity parameters set, as the only feasibly admissible within the current methodical proposal, is suggested.