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

TL;DR

This paper presents exact solutions for position-dependent mass charged particles in magnetic and flux fields, analyzing both free and potential-influenced cases with novel spectroscopic structures and energy level crossings.

Contribution

It provides new exact analytical solutions for PDM particles in complex fields and potentials, including Yukawa and Kratzer types, using the NU method.

Findings

Exact eigenvalues and eigenfunctions derived for specific PDM scenarios.

Identification of energy level crossings in the spectra.

Comparison between free and potential-influenced PDM particles.

Abstract

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