New Solvable Shape-Invariant Potentials for Position-Dependent Effective Mass

TL;DR

This paper introduces four new exactly solvable, shape-invariant potentials with position-dependent effective mass, expanding the set of solvable models in quantum mechanics and providing explicit energy spectra and wavefunctions.

Contribution

It presents four novel shape-invariant potentials with position-dependent mass, derived using a specific superpotential ansatz, and compares their spectra with existing literature.

Findings

Four new exactly solvable potentials identified

Explicit energy spectra and wavefunctions derived

Results align with and extend previous models

Abstract

Four new exactly solvable, real and shape-invariant potentials associated with a position-dependent effective mass are generated within the concept of shape-invariant potentials using a specific ansatz for superpotential. The accompanying energy spectra of the bound-state and the ground-state wavefunction are obtained algebraically as a function of free parameters and the results are compared with those of others works in the litterature.