Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass

TL;DR

This paper derives exact solutions for the Schrödinger equation with modified Kratzer and Morse potentials considering a position-dependent mass, providing explicit energy levels and wavefunctions for various angular momenta.

Contribution

It introduces a method to obtain exact bound state solutions for these potentials with position-dependent mass using point canonical transformations.

Findings

Explicit energy eigenvalues for modified Kratzer and Morse potentials.

Wavefunctions corresponding to these potentials.

Applicability to any angular momentum states.

Abstract

Exact solutions of Schrodinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied. PACS numbers: 03.65.-w; 03.65.Ge; 12.39.Fd Keywords: Morse potential, Kratzer potential, Position-dependent mass, Point canonical transformation, Effective mass Schr\"{o}dinger equation.