Approximate solutions and thermodynamic properties of a potential model

The solution of the radial Schrödinger equation for a Pὃschl-Teller type of potential with two main parameters is obtained via the supersymmetric approach. The energy equation and its corresponding wave function are obtained explicitly. The energy equation obtained was used to calculate the partition function via the Poisson summation formula. The calculated partition was used to studied the enthalpy, Gibbs free energy and entropy of the system. The result obtained showed that the two parameters have the same effect on the energy of the system but different effects on the thermodynamic properties. It was also shown that the rise in temperature of the system only increases enthalpy but decreases partition function, Gibbs free energy an entropy.