Solution of the Woods-Saxon Potential and its Application for Study of Thermodynamic Properties

Abstract

This work presents an exact analytical solution for the Schrödinger equation with the Woods-Saxon potential. To achieve this, the factorization method is utilized with the Pekeris approximation applied to the centrifugal potential for arbitrary  states. The resulting solution provides both the wave functions of the potential expressed in the hypergeometric function and the energy eigenvalues. Additionally, the study calculates the thermodynamic properties of the Woods-Saxon potential in its classical limit, including the vibrational partition function, mean vibrational energy, vibrational specific heat, vibrational mean free energy, and vibrational entropy.