PDM-charged particles in PD-magnetic plus Aharonov–Bohm flux fields: Unconfined “almost-quasi-free” and confined in a Yukawa plus Kratzer exact solvability

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 with m(r→)=g(ρ)=ηf(ρ)exp(−δρ) (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fields B→=B∘(μ/ρσ)z^. Under such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential, V(r→)=0) endowed with g(ρ)=η/ρ and g(ρ)=η/ρ2. Both yield exactly solvable Schrödinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle with g(ρ)=ηexp(−δρ)/ρ 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 V(ρ)=−V∘exp(−δρ)/ρ−V1/ρ+V2/ρ2. 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-freePDM-charged particle with g(ρ)=η/ρ for V∘=V1=V2=0=δ. Energy levels crossings are also reported.