The determination of eigenvalues of Klein-Gordon equation with position dependent mass (PDMKG) for exponential type potentials

The bound-state solution of Klein-Gordon equation calculated using Asymtotic Iteration Method for some exponential-type scalar and vector potential functions such as Morse potential and Wood-Saxon potential. The eigenvalues and eigenfunctions of corresponding potentials are obtained for constant mass and for the exponential type of position dependent mass functions. Also, the eigenvalues are analyzed for pure scalar potential and the vector potential in addition to the equal scalar and vector potential with respect to ? values. The bound state eigenfunctions calculated after the operations are obtained in terms of the confluent hypergeometric function using the wave function generator.Keywords: Position dependent mass Klein-Gordon equation, eigenvalue, eigenfunction, asymptotic iteration method, scalar potential, vector potential, exponential potentials, Wood-Saxon potential.