Eigen Solution and Thermodynamic Properties of Manning Rosen Plus Exponential Yukawa Potential

TL;DR

This paper analytically solves the Schrödinger equation for a combined Manning Rosen and exponential Yukawa potential, deriving energy levels and thermodynamic properties, and validates results with numerical computations.

Contribution

It presents a novel analytical solution for bound states and thermodynamic properties of this combined potential using the Nikiforov-Uvarov method.

Findings

Bound state energies increase with quantum number.

Thermodynamic properties align with existing literature.

Numerical energies computed for various screening parameters.

Abstract

In this work, we obtained analytical bound state solution of the Schr\"odinger equation with Manning Rosen plus exponential Yukawa Potential using parametric Nikiforov-Uvarov method (NU). We obtained the normalized wave function in terms of Jacobi polynomial. The energy eigen equation was determined and presented in a compact form. The study also includes the computations of partition function and other thermodynamics properties such as vibrational mean energy ({\mu}), vibrational heat capacity (c), vibrational entropy (s) and vibrational free energy (F). Using a well design maple programme, we obtained numerical bound state energies for different quantum states with various screening parameters: {\alpha}=0.1,0.2,0.3,0.4 and 0.5. The numerical results showed that the bound state energies increase with an increase in quantum state while the thermodynamic plots were in excellent agreement to work of existing literature.