Relativistic spinless particles with position dependent mass: Bound states and scattering phase shifts

The scattering and bound states of relativistic spinless particles with position-dependent mass are investigated in the framework of the improved Frost-Musulin potential, which is used to explain some properties of diatomic molecules. After we obtain approximate analytical solution of the Klein-Gordon equation, we find the normalized wave functions in terms of the hypergeometric functions in order to deal with the bound and the scattering states. We also analyze the scattering phase shifts and the bound states numerically.