International Research Journal of Pure and Applied Physics Vol.5, No.3, pp.27-32, August 2017 ___Published by European Centre for Research Training and Development UK (www.eajournals.org) 27 ISSN 2055-009X(Print), ISSN 2055-0103(Online) WKB SOLUTIONS FOR QUANTUM MECHANICAL GRAVITATIONAL POTENTIAL PLUS HARMONIC OSCILLATOR POTENTIAL H. Louis 1&4 , B. I. Ita 1 , N. A. Nzeata-Ibe 1 , P. I. Amos 2 , I. Joseph 2 , A. N Ikot 3 and T. O. Magu 1 1 Physical/Theoretical Chemistry Unit, Department of Pure and Applied Chemistry, University of Calabar, Calabar, Cross River State, Nigeria. 2 Department of Chemistry, ModibboAdama University of Technology, Yola, Adamawa State, Nigeria. 3 Theoretical Physics Group, Department of Physics, University of Uyo, Uyo,AkwaIbom State, Nigeria. 4 CAS Key Laboratory for Nanosystem and Hierarchical Fabrication, CAS Centre for Excellence in Nanoscience, National Centre for Nanoscience and Technology, University of Chinese Academy of Sciences, Beijing, China. ABSTRACT: We have obtained the exact energy spectrum for a quantum mechanical gravitational potential, plus a harmonic oscillator potential, via the WKB approach. Also a special case of the potential has been considered and their energy eigen value obtained. KEYWORDS: Schrodinger Equation, Harmonic Oscillator Potential, Quantum Mechanical Gravitational Potential, Bohr Sommerfeld Wkb Approximation. INTRODUCTION The bound state solutions of the Schrodinger equation (SE) are only possible for some potentials of physical interest [1-3]. These solutions could be exact or approximate and they normally contain all the necessary information for the quantum system. Quite recently, several authors have tried to solve problems that involve obtaining the exact or approximate solutions of the Schrodinger equation for a number of special potentials using different methods [4-7]. One of the earliest and simplest methods of obtaining approximate eigenvalues to the one- dimensional Schrodinger equation in the limiting case of large quantum numbers was originally proposed by Wentzel, Kramers, and Brillouin known as the WKB approximation method [8]. Considering the one dimensional radial Schrodinger equation of the form [9] for s-wave case where  = Ͳ, it means that the problem has no minimum value and also doesn’t have the left turning point from the physical point of view [10] and the energy obtained would not produce a stable bound state. In order for the physical system to have a stable bound state, we use the Langer correction ሺ + ͳሻ → ቀ + ଵ ଶ ቁ ଶ in the centrifugal term of the radial Schrodinger equation [8]. The replacement of ሺ + ͳሻ → ቀ + ଵ ଶ ቁ ଶ regularizes the radial WKB wave function at the origin and ensure correct asymptotic behaviour at large quantum numbers. It was observed by Langer [11] that the reason for this modification arose from the fact that the quantization condition for the one-dimensional problem was derived under the assumption that the wave function approached zero for → ±∞ , whereas the radial part of the solution approached zero for → ݎͲ and r → ∞.