         1, 2, 3 Theoretical Physics Group, Department Of Physics, University Of Uyo, Nigeria  June 2011 4 Department of Physics, University of Calabar, Nigeria. e-mail: ndemikot2005@yahoo.com Analytical Solutions of Schrödinger Equation with Two- Dimensional Harmonic Potential in Cartesian and Polar Coordinates Via Nikiforov-Uvarov Method                    ABSTRACT: We evaluate the exact solutions of the Schrödinger equation with two-dimensional harmonic oscillator in Cartesian and Polar – Co-ordinate via the Nikiforov-Uvarov method. The wave functions and the corresponding energy spectrum of the potential are obtained analytically. KEYWORDS: Nikiforov-Uvarov Method, Two-Dimensional Harmonic Potential, Schrödinger Equation. I. INTRODUCTION The search for exact solutions of wave equations, whether non-relativistic or relativistic has been an important research area in physics and chemistry. The bound state solutions of the radial Schrödinger equation is very important in non-relativistic quantum mechanics since the wave function and its associated eigenvalues contain all the necessary information to describe a quantum system fully. Different methods have been developed in solving the Schrödinger equation with various potentials [1-7]. Among such methods include the super symmetric approach [8-9], the variational method [10], the algebraic method [11], the shape invariant method [12], the asymptotic iteration method (AIM) [13-15] and the Nikiforov–Uvarov method (NU) [16-20]. However, since the Schrödinger equation is a second order differential, the NU method is more suitable for obtaining analytical solutions to such a differential equation. Obtaining the bound state solutions of the Schrödinger equation with two dimensional harmonic potential will significantly enriched our knowledge of atomic and sub-atomic system [21]. Satisfied with the Nikiforov-Uvarov (NU) method through comparisons with other methods, we are tempted to solve the time independent Schrodinger equation for two dimensional harmonic potential in Cartesian and polar co-ordinate. This potential plays a vital role in many branches of physics such as atomic, molecular and chemical physics. The organization of the paper is as follows. In section2, we review the NU method. In Section 3, we obtain the exact solutions of the Schrodinger equation in Cartesian co-ordinate. Factorization method is presented in section 4. In section 5, we obtain the exact solutions of the radial and angle- dependent Schrodinger equations. Finally, we give a brief conclusion in section 6.