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We solve the Schr\"odinger equation with a position-dependent mass (PDM)charged particle interacted via the superposition of the Morse and Coulombpotentials and exposed to external magnetic and Aharonov-Bohm (AB) flux fields.The non-relativistic bound state energies together with their wave functionsare calculated for two spatially-dependent mass distribution functions. We alsostudy the thermal quantities of such a system. Further, the canonical formalismis used to compute various thermodynamic variables for second choosing mass byusing the Gibbs formalism. We give plots for energy as a function of variousphysical parameters. The behavior of the internal energy, specific heat andentropy as functions of temperature and mass density parameter in theinverse-square mass case for different values of magnetic field are shown.

Approximate energy states and thermal properties of a particle with position-dependent mass in external magnetic fields