d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

TL;DR

This paper extends the point canonical transformation method to d-dimensional quantum systems with position-dependent mass, enabling exact solutions for various potentials and mass configurations.

Contribution

It provides a generalized framework for solving the Schrödinger equation with position-dependent mass in multiple dimensions, including explicit examples.

Findings

Exact energy eigenvalues obtained for multiple potentials.

Explicit eigenfunctions derived for different mass distributions.

Demonstrated applicability to various quantum systems.

Abstract

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.