In this paper, we have solved the Schrodinger equation of hyperbolic function position dependent mass for a Modified Hyperbolic Pöschl-Teller potential under external hyperbolic magnetic and AB forces using Laplace transform and Hypergeometry method. The second order differential equation of Schrodinger equation reduced to first order differential equation by using Laplace transform. Then radial part of the system was solved by using hypergeometric function. The eigen function and eigen energy values are obtained, where the energy spectra are influenced by the quantum number, potential parameters, and external magnetic with the various of B and AB force are affected depending on the diatomic molecules for certain condition.
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