Rotation and vibration of diatomic molecule in the spatially-dependent mass Schrodinger equation with generalized q-deformed Morse potential

TL;DR

This paper derives approximate analytical solutions for the spatially-dependent mass Schrödinger equation with a generalized q-deformed Morse potential, including centrifugal terms, for diatomic molecules, and compares results with other methods.

Contribution

It introduces a parametric generalization of the NU method combined with Pekeris approximation to solve the equation analytically for diatomic molecules with spatially-dependent mass.

Findings

Energy eigenvalues for H2, LiH, HCl, and CO match well with other methods.

Closed-form wave functions are obtained for arbitrary vibrational and rotational states.

The model extends to constant mass case when delta=0.

Abstract

The analytic solutions of the spatially-dependent mass Schrodinger equation of diatomic molecules with the centrifugal term l(l+1)/r2 for the generalized q-deformed Morse potential are obtained approximately by means of a parametric generalization of the Nikiforov-Uvarov (NU) method combined with the Pekeris approximation scheme. The energy eigenvalues and the corresponding normalized radial wave functions are calculated in closed form with a physically motivated choice of a reciprocal Morse-like mass function, m(r)=m0/(1-deltae^{-a(r-r_{e})})2, 0<delta<1, where a and r_{e} are the range of the potential and the equilibrium position of the nuclei. The constant mass case when delta=0 is also studied. The energy states for H2, LiH, HCl and CO diatomic molecules are calculated and compared favourably well with those obtained by using other approximation methods for arbitrary vibrational n and rotational l quantum numbers.