The general solutions of Schrödinger equation for non-central potential are obtained by using Nikiforov-Uvarov method. The Schrödinger equation with general non-central potential is separated into radial and angular parts and energy eigenvalues and eigenfunctions for these potentials are derived analytically. Non-central potential is reduced to Coulomb and Hartmann potential by making special selections, and the obtained solutions are compared with the solutions of Coulomb and Hartmann ring-shaped potentials given in literature.

We present an alternative and simple method for the exact solution of the Klein-Gordon equation in the presence of the non-central equal scalar and vector potentials by using Nikiforov-Uvarov (NU) method. The exact bound state energy eigenvalues and corresponding eigenfunctions are obtained for a particle bound in a potential of V (r, θ) = α r + β r 2 sin 2 θ + γ cos θ r 2 sin 2 θ type.

A simple exact analytical solution of the relativistic Duffin-Kemmer-Petiau equation within the framework of the asymptotic iteration method is presented. Exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the Coulomb potentials. As a non-trivial example, the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method.

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

Using the Nikiforov-Uvarov method, an application of the relativistic Duffin-Kemmer-Petiau equation in the presence of a deformed Hulthen potential is presented for spin zero particles. We derived the first-order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunctions to be evaluated by using of the Nikiforov-Uvarov method that can be written in terms of the hypergeometric polynomials.