The unified treatment of the non-relativistic bound state solutions, thermodynamic properties, and expectation values of exponential-type potentials

Abstract

In this paper, we obtained the analytical N-dimensional bound state solutions of exponential-type potential functions using the semi-classical Wentzel–Kramers–Brillouin (WKB) approximation method with an improved approximation to the orbital centrifugal barrier. Furthermore, we derived the partition function with the associated thermodynamic properties. We calculated the expectation values (〈1/r2〉) via the Hellmann–Feynman theorem. Our results for the energy levels are in excellent agreement with the best available results obtained by other methods in the existing literature. The variations of the thermodynamic functions with the temperature parameter (β) agree very well with the other results obtained under different potential energy functions. The expectation values conformed to the ones obtained by another approach in previous work. This work demonstrates the exactness of the leading-order WKB approximation.