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 <cite>26</cite>, along with the PDM-momentum operator <cite>27</cite>, and report separability under radial cylindrical and azimuthal symmetrization settings. For the radial Schrödinger part, we transform it into a radial one-dimensional Schrödinger-type and use two PDM settings to report on the exact solvability of PDM charged particles moving in three fields: magnetic, Aharonov-Bohm flux, and pseudoharmonic potential fields. Next, we consider the radial Schrödinger part as is and use the biconfluent Heun differential forms for two PDM settings to report on the conditionally exact solvability of 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-dimensional z-dependent Schrödinger part on the overall eigenvalues and eigenfunctions, for all examples, using two z-dependent potential models (infinite potential well and Morse-type potentials).

arXiv comment12 pages, no figures

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Cited by in corpus (2)

• Landau Quantization for an electric quadrupole moment of Position-Dependent Mass Quantum Particles interacting with Electromagnetic fields
• PDM-charged particles in PD-magnetic plus Aharonov-Bohm flux fields: unconfined "almost-quasi-free" and confined in a Yukawa plus Kratzer exact solvability