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 l 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. Keywords: Woods-Saxon Potential, Schrodinger equation, Thermodynamic properties, Factorization method. PACS numbers: 11.15.Ha, 12.38.Gc.