Exact bound state solution of the Klein Gordon equation with a position-energy dependent mass and a Coulomb-like energy dependent potential energy. (arXiv:1907.04760v1 [quant-ph])

In this manuscript, we investigate the exact bound state solution of the
Klein Gordon equation with an energy-dependent Coulomb-like potential energy in
the presence of position-energy dependent mass. First, we examine the case
where the mixed vector and scalar potential energy possess equal magnitude and
equal sign. Then, we extend the investigation with the cases where the mixed
potential energies have equal magnitude and opposite sign. Furthermore, we
study pure scalar and pure vector cases. In each case, we derive an analytic
expression of the energy spectrum by employing the asymptotic iteration method.
We obtain a non-trivial relation between the tuning parameters which lead the
examined problem to a constant mass one. Finally, we employ the Secant method
to calculate the energy spectra. We use the calculated spectra and show that
the unnormalized wave functions satisfy the boundary conditions. We conclude
the manuscript with a comparison of the calculated energy spectra versus tuning
parameters.

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