The investigation of the effects of velocity dependent potential in the solution of wave equation

ABSTRACT THE INVESTIGATION OF THE EFFECTS OF VELOCITY DEPENDENT POTENTIAL IN THE SOLUTION OF WAVE EQUATION BERK ATEŞ, Yıldız Ph.D in Engineering Physics Supervisor: Prof. Dr. Eser OLĞAR February 2020 88 pages In this thesis, the effect of the velocity-dependent potential is taken into consideration in order to obtain the solution of Schrödinger equation (SE) for different physical potentials. By choosing form factors as three different cases such as ε(r)=γρ_0,ε(r)=γr and ε(r)=γr^2, the velocity-dependent potential is determined and the energy eigenvalues and eigenfunction are obtained for any quantum numbers n and l. During all calculations, the well-known method Nikiforov-Uvarov (NU) method is used. It is seen that by taking γ=0, the obtained results are reduced to results of velocity-independent potential case which are in good agreement with those of in literature. The variations of energy eigenvalues are tabulated and graphed with respect to quantum numbers n and l. Key Words: Velocity-Dependent Potentials, Analytical Solution, Numerical Solution, Nikiforov-Uvarov Method.