WKB Energy Expression for the Radial Schrödinger Equation with a Generalized Pseudoharmonic Potential
E. Omugbe *
Department of Physics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
O. E. Osafile
Department of Physics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
I. B. Okon
Theoretical Physics Group, Department of Physics, University of Uyo, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we applied the semi-classical quantization approximation method to solve the radial Schrödinger equation with a generalized Pseudoharmonic potential. The four turning points problem within the framework of the Wentzel-Kramers-Brillouin (WKB) method was transformed into two turning points and subsequently, the energy spectrum was obtained. Some special cases of the generalized Pseudoharmonic potential are presented. The WKB approximation approach reproduces the exact energy expression obtained with several analytical methods in the literature. The values of the energy levels for some selected diatomic molecules (N2, CO, NO, CH) obtained numerically are in excellent agreement with those from previous works in the literature.
Keywords: Schrödinger equation, WKB approximation method, Pseudoharmonic potential