Approximate L-State Solution of the Rotating Trigonometric P\"oschl-Teller Potential

TL;DR

This paper derives approximate analytical solutions for the Schrödinger equation with the rotating trigonometric P"oschl-Teller potential, relevant for diatomic molecular vibrations, using the Nikiforov-Uvarov method, and compares with known potentials.

Contribution

It provides the first approximate closed-form solutions for the rotating trigonometric P"oschl-Teller potential using the NU method, including energy eigenvalues and eigenfunctions.

Findings

Solutions reduce to Kratzer potential in low screening region

Numerical results for diatomic molecules demonstrate the method's effectiveness

Eigenvalues and eigenfunctions obtained for arbitrary angular momentum states

Abstract

The trigonometric P\"oschl-Teller (PT) potential describes the diatomic molecular vibration. We have obtained the approximate solutions of the radial Schr\"odinger equation (SE) for the rotating trigonometric PT potential using the Nikiforov-Uvarov (NU) method. The energy eigenvalues and their corresponding eigenfunctions are calculated for arbitrary -states in closed form. In the low screening region, when the screening parameter the potential reduces to Kratzer potential. Further, some numerical results are presented for several diatomic molecules.