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Using azimuthally symmetrized cylindrical coordinates, we consider someposition-dependent mass (PDM) charged particles moving in position-dependent(PD) magnetic and Aharonov-Bohm flux fields. We focus our attention onPDM-charged particles (i.e., the PDM is only radially dependent) moving in aninverse power-law-type radial PD-magnetic fields. Under such settings, weconsider two almost-quasi-free PDM-charged particles (i.e., no interactionpotential). Both yield exactly solvable Schr\"odinger equations of Coulombicnature but with different spectroscopic structures. Moreover, we consider aYukawa-type PDM-charged particle moving not only in the vicinity of thePD-magnetic and Aharonov-Bohm flux fields but also in the vicinity of a Yukawaplus a Kratzer type potential force field. For this particular case, we use theNikiforov-Uvarov (NU) method to come out with exact analytical eigenvalues andeigenfunctions. Which, in turn, recover those of the almost-quasi-freePDM-charged particle. Energy levels crossings are also reported.

chinese journal of physics

PDM-charged particles in PD-magnetic plus Aharonov-Bohm flux fields:  unconfined "almost-quasi-free" and confined in a Yukawa plus Kratzer exact  solvability