Cent. Eur. J. Phys. • 6(3) • 2008 • 685-696 DOI: 10.2478/s11534-008-0024-2 Central European Journal of Physics Exact solutions of the D-dimensional Schrödinger equation for a ring–shaped pseudoharmonic potential Research Article Sameer M. Ikhdair 1* , Ramazan Sever 2† 1 Department of Physics, Near East University, Nicosia, TRNC, Mersin-10, Turkey 2 Department of Physics, Middle East Technical University, 06531 Ankara, Turkey Received 10 October 2007; accepted 6 December 2007 Abstract: A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring- shaped potential, is solved. It has the form V (θ)= 1 8 κ 2     -    2 + β cos 2 θ  2 sin 2 θ  The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions. PACS (2008): 03.65.-w, 03.65.Fd, 0365.Ge, 04.20.Jb Keywords: energy eigenvalues and eigenfunctions • pseudoharmonic potential • ring-shaped potential • non-central potentials • Nikiforov and Uvarov method © Versita Warsaw and Springer-Verlag Berlin Heidelberg. 1. Introduction The solution of the fundamental dynamical equations is an interesting phenomenon in many fields of physics and chemistry. Obtaining the exact  -state solutions of the Schrödinger equation (SE) is possible only for a few po- tentials. Hence approximation methods are used to obtain their solutions [1–4]. So far, much work in this direction has been done for solving the stationary SE with anhar- monic potentials in two dimensions (2D) and three dimen- sions (3D)[5–10] with many applications to molecular and * E-mail: sikhdair@neu.edu.tr † E-mail: sever@metu.edu.tr chemical physics. The study of the SE with these poten- tials provides us with insight into the physical problem un- der consideration. However, the study of bound-states of the SE for some of these potentials in arbitrary dimensions D is fundamental to understanding the molecular spectrum of a diatomic molecule [11, 12]. The Harmonic oscillator [13, 14] and H-atom (Coulombic) [13–15] problems have been thoroughly studied in D-dimensional space quan- tum mechanics for any angular momentum quantum num- ber  These two problems are related with each other and hence the respective resulting second-order differen- tial equations both have normalized orthogonal polyno- mial function solutions. In addition, the pseudoharmonic potential may be used for the energy spectrum of linear and non-linear systems [16– 685