We need to solve a suitable exponential form of the position-dependent mass (PDM) Schrodinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the influence of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for spatially-dependent mass distribution function of a physical interest. A few plots of some numerical results to the energy are shown.
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