Modified l-states of diatomic molecules subject to central potentials plus an angle-dependent potential

TL;DR

This paper derives modified angular momentum states for diatomic molecules by solving the Schrödinger equation with central and angle-dependent potentials, providing explicit bound state energies for various molecules using the NU method.

Contribution

It introduces a novel approach to incorporate angle-dependent potentials into diatomic molecule models, modifying the angular momentum quantum number and solving for bound states.

Findings

Modified angular momentum quantum number due to angle-dependent potential

Explicit bound state energies for several diatomic molecules

Application of NU method to combined central and angle-dependent potentials

Abstract

We present modified $\ell$-states of diatomic molecules by solving the radial and angle-dependent parts of the Schr\"odinger equation for central potentials, such as Morse and Kratzer, plus an exactly solvable angle-dependent potential $V_{\theta}(\theta)/r^2$ within the framework of the Nikiforov-Uvarov (NU) method. We emphasize that the contribution which comes from the solution of the Schr\"odinger equation for the angle-dependent potential modifies the usual angular momentum quantum number $\ell$. We calculate explicitly bound state energies of a number of neutral diatomic molecules composed of a first-row transition metal and main-group elements for both Morse and Kratzer potentials plus an angle-dependent potential.