Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems

TL;DR

This paper solves the D-dimensional Schrödinger equation with position-dependent mass for pseudoharmonic and modified Kratzer potentials using point canonical transformation, providing exact bound state solutions and energy spectra.

Contribution

It introduces a method to obtain exact solutions for PDEM Schrödinger equations with specific molecular potentials in multiple dimensions.

Findings

Exact energy eigenvalues derived for pseudoharmonic and modified Kratzer potentials.

Wave functions explicitly constructed for various dimensions.

Method applicable to other potentials with position-dependent mass.

Abstract

We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($D\geq 2$) Schr\"{o}dinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.