Analytical solution to position dependent mass Schr\"odinger equation

TL;DR

This paper presents an analytical solution to the position-dependent mass Schrödinger equation and explores its applications in scattering problems and atomic system analogies.

Contribution

It introduces a new analytical method for solving the PDMSE and demonstrates its use in scattering and atomic system analogies.

Findings

Derived an explicit analytical solution for PDMSE.

Applied the solution to scattering problems with position-dependent mass.

Revealed structural analogy between PDMSE and two-level atomic systems.

Abstract

Using a recently developed technique to solve Schr\"odinger equation for constant mass, we studied the regime in which mass varies with position i.e position dependent mass Schr\"odinger equation(PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass $m(x)$ particle scattered by a potential $\mathcal{V}(x)$. We also studied the structural analogy between PDMSE and two-level atomic system interacting with a classical field.