Position-dependent mass charged particles in magnetic and Aharonov-Bohm flux fields: separability, exact and conditionally exact solvability

Abstract

Using cylindrical coordinates, we consider position-dependent mass (PDM) charged particles moving under the influence of magnetic, Aharonov-Bohm flux, and a pseudoharmonic or a generalized Killingbeck-type potential fields. We implement the PDM minimal coupling recipe (Mustafa in J Phys A Math Theor 52:148001, 2019), along with the PDM-momentum operator (Mustafa and Algadhi in Eur Phys J Plus 134:228, 2019), and report separability under radial cylindrical and azimuthal symmetrization settings. For the radial Schrodinger part, we transform it into a radial one-dimensional Schrodinger-type and use two PDM settings, g(rho)=eta rho(2) and g(rho) = eta/rho(2), to report on theexact solvabilityof PDM charged particles moving in three fields: magnetic, Aharonov-Bohm flux, and pseudoharmonic potential fields. Next, we consider the radial Schrodinger part as is and use the biconfluent Heun differential forms for two PDM settings, g(rho) = lambda rho and g (rho) = lambda/rho(2), to report on theconditionally exact solvabilityof our PDM charged particles moving in three fields: magnetic, Aharonov-Bohm flux, and generalized Killingbeck potential fields. Yet, we report the spectral signatures of the one-dimensionalz-dependent Schrodinger part on the overall eigenvalues and eigenfunctions, for all examples, using twoz-dependent potential models (infinite potential well and Morse-type potentials).