Exact mapping between charge-monopole and position-dependent effective mass systems via Pauli equation

The main purpose of this work is to reproduce a quantum system charge-monopole utilizing position-dependent effective mass (PDM) system in the nonrelativistic regime via the Pauli equation. In this case, we substitute the exact charge-monopole wavefunction into the free PDM Pauli equation and then solve it for the mass distribution considering a radial dependence only, i.e., M = M(r). The resulting equations are nonlinear, and in such cases, we were able to numerically solve them, fixing theta(0) and considering specific values of mu and m satisfying a given condition. The mapping was studied for eigenvalues starting from the minimal value j = mu - 1/2. Published under license by AIP Publishing.