A new approach to the exact solutions of the effective mass Schrodinger equation

TL;DR

This paper presents an exact solution method for the effective mass Schrödinger equation using the Nikiforov-Uvarov approach, including transformations for Morse potential and wave function parameters, advancing quantum potential analysis.

Contribution

It introduces a novel exact solution technique for the effective mass Schrödinger equation, incorporating a free parameter and transformations for specific potentials.

Findings

Exact energy eigenvalues obtained for given potentials.

Wave functions derived explicitly using the Nikiforov-Uvarov method.

Solutions applicable to Morse potential and transformations from constant mass cases.

Abstract

Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrodinger equation is also solved for the Morse potential transforming to the constant mass Schr\"{o}dinger equation for a potential. One can also get solution of the effective mass Schrodinger equation starting from the constant mass Schrodinger equation.