Eigensolution and Thermodynamic Properties of Standard Coulombic Potential

The study investigates the combination of the Coulomb potential with itself (standard Coulombic potential) under the nonrelativistic wave equation. The energy equation and the corresponding unnormalized radial wave function are obtained using the parametric Nikiforov–Uvarov method. This is achieved by applying a Green–Aldrich approximation scheme to the centrifugal term. The resulting energy equation is utilized to calculate the partition function, from which thermodynamic properties such as mean energy, specific heat capacity, entropy, and free energy are derived. Numerical results are generated for the standard Coulombic potential and its special cases, including Coulomb potential with negative potential strength and Coulomb potential with positive potential strength. The study reveals that the system’s energy is fully bounded. Notably, the two special cases, representing Coulomb–Coulomb potentials with positive and negative potential strengths, yield equal results when the strengths are equal but opposite in sign. The thermodynamic properties align with existing literature but exhibit some unique behaviors.