PDM-Charged Quantum Particles Moving in Magnetic Fields

The classical and quantum mechanical correspondence for constant mass settings is used, along with some nonlocal point transformation (NPT), to find the position-dependent mass (PDM) classical and quantum Hamiltonians. Consequently, the PDM-momentum operator is constructed. The same recipe is followed to identify the form of the PDM-minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. Using azimuthally symmetrized cylindrical coordinates, some PDM-charged particles moving in magnetic (constant or position-dependent (PD)) and Aharonov-Bohm (AB) flux fields along with some interaction potentials are considered. Their separability and solvability under PDM-settings is also reported. Systems of PDM-charged particles moving in three fields: constant magnetic, AB-flux, and pseudoharmonic oscillator potential, or generalized Killingbeck potential fields are solved for different radial cylindrical PDM settings. Spectral signatures of the one-dimensional z-dependent Schr¨odinger part on the overall eigenvalues and eigenfunctions, are reported using two z-dependent potential models (infinite potential well and Morse-type potentials). PDM-charged particles moving in an inverse power-law-type radial PD-magnetic fields are considered. Under such settings, the exact solutions of almost-quasi-free PDM-charged particles (i.e., no interaction potential) endowed with two type of radial cylindrical PDM settings are obtained. Furthermore, a Yukawa-type PDM-charged particle with a specific PDM setting moving in PD-magnetic and AB-flux fields along with Yukawa plus Kratzer type potential force fields is analyzed (using the Nikiforov-Uvarov (NU) method) to come out with exact solutions of the system. Exact or conditionally exact eigenvalues and eigenfunctions are analytically obtained. Keywords: position-dependent mass Hamiltonian, point transformation, PDM - momentum operator, PDM minimal-coupling, cylindrical coordinates, constant magnetic and position-dependent magnetic fields, Aharonov-Bohm flux field, almost-quasi-free PDM-charged particles, pseudo-harmonic osillator and Killingbeck potentials, Yukawa-plus-Kratzer potential, Nikiforov-Uvarov exact solvability.