Construction of Klein-Gordon equation (KG) with position dependent mass and application to the physical systems

In this study, Klein-Gordon equation with position dependent mass is formulated via Einstein?s theory of relativity. The relation between scalar and vector potentials is defined as S(x)=(ß-1)V(x) in order to be solved in the bound state solutions. Asymptotic iteration method, one of the most common methods to solve Klein-Gordon type equations, is chosen and explained.The solutions of the equations are analyzed for both position-dependent and constant mass situations and their eigenvalues and eigenfunctions are derived. Before the solution of Klein-Gordon equations with position-dependent mass, the validity of asymptotic iteration method for Klein-Gordon equation with constant mass is examined. The spectrums are obtained by applying the method to Morse potential, Harmonic oscillator potential and Kratzer potential for the Klein-Gordon equation with constant mass, and applied to Kratzer potential and exponential potentials for Klein-Gordon equation with position-dependent mass.Key Words: Position dependent mass Klein-Gordon equation, eigenvalue, eigenfunction, asymptotic iteration method, scalar potential, vector potential.