Eigensolution and Thermodynamic Properties of Standard Coulombic Potential

Abstract

The Combination of Coulomb potential with itself(standard Coulombic potential) is studied under the non-relativistic wave equation. The energy equation and its corresponding un-normalized redial wave are obtained using parametric Nikiforov-Uvarov method by applying a Green-Aldrich approximation scheme to the centrifugal term. The energy equation obtained was used to calculated the partition function from where the thermodynamic properties such as the mean energy, specific heat capacity, entropy and free energy are calculated. Numerical results are generated for the standard Coulombic potential and its special cases. The special cases are Coulomb potential with negative potential strength and the other is also Coulomb potential with positive potential strength. The study showed that the energy of the system is fully bounded. It is noted that the two special cases which are Coulomb-Coulomb potentials with positive and negative potential strengths are equal provided the strength are equal but opposite in sign. The thermodynamic properties aligned with those of the literature but has some unique behaviours.