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) over right arrow) = g(rho)= eta f (rho)exp(-delta rho) (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fields B = (B) over right arrow (o) (mu/rho(sigma))(z) over cap. Under such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential, V((r) over right arrow) = 0) endowed with g(rho)= eta/rho and g(rho)= eta/rho(2). Both yield exactly solvable Schrodinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle with g(rho) = eta exp(-delta rho)/rho 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 (rho) =-V(o)exp(-delta rho)/rho- V-1/rho + V-2/rho(2). 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-quasifree-PDM-charged particle with g(rho) = n/rho for V-o = V-1 = V-2 = 0 = delta. Energy levels crossings are also reported.