Effective Schroedinger equation with general ordering ambiguity position-dependent mass Morse potential

TL;DR

This paper analytically solves the position-dependent mass Schrödinger equation with Morse potential using the NU method, providing explicit bound-state energies and wave functions for various molecules and mass functions.

Contribution

It introduces a method to obtain exact solutions for the generalized Schrödinger equation with position-dependent mass and Morse potential, including specific ordering ambiguities.

Findings

Explicit bound-state energies for diatomic molecules.

Analytical wave functions for various quantum states.

Comparison of constant and position-dependent mass cases.

Abstract

We solve the parametric generalized effective Schr\"odinger equation with a specific choice of posi-tion-dependent mass function and Morse oscillator potential by means of the Nikiforov-Uvarov (NU) method combined with the Pekeris approximation scheme. All bound-state energies are found explicitly and all corresponding radial wave functions are built analytically. We choose the Weyl or Li and Kuhn ordering for the ambiguity parameters in our numerical work to calculate the energy spectrum for a few and diatomic molecules with arbitrary vibration and rotation quantum numbers and different position-dependent mass functions. Two special cases including the constant mass and the vibration s-wave (l =0) are also investigated.