Approximate Analytical Solutions to Relativistic and Nonrelativistic P\"{o}schl-Teller Potential with its Thermodynamic Properties

TL;DR

This paper uses the asymptotic iteration method to solve Schrödinger and Dirac equations with Pöschl-Teller potentials, analyzing their energy spectra and thermodynamic properties across relativistic and nonrelativistic regimes.

Contribution

It provides approximate analytical solutions for both Schrödinger and Dirac equations with Pöschl-Teller potential, including thermodynamic analysis at high temperatures.

Findings

Solutions converge in nonrelativistic limits

Calculated vibrational energy levels for diatomic molecules

Analyzed thermodynamic functions like energy, heat capacity, and entropy

Abstract

We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrodinger system. Rotational-Vibrational energy eigenvalues of some diatomic molecules are calculated. Some special cases of interest are studied such as s-wave case, reflectionless-type potential and symmetric hyperbolic PT potential. Furthermore, we present a high temperature partition function in order to study the behavior of the thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S.