Nonrelativistic Green's function for systems with position-dependent mass

TL;DR

This paper derives the two-point Green's function for nonrelativistic systems with position-dependent mass by transforming the problem into known solvable Schrödinger equations, focusing on the oscillator class.

Contribution

It introduces a method to obtain Green's functions for position-dependent mass systems via point canonical transformation, expanding solvable models.

Findings

Green's functions derived for specific mass distributions

Method applicable to oscillator class systems

Provides explicit examples and solutions

Abstract

Given a spatially dependent mass we obtain the two-point Green's function for exactly solvable nonrelativistic problems. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger equations with constant mass using point canonical transformation. The one-dimensional oscillator class is considered and examples are given for several mass distributions.