Study of the radial Schrodinger equation with external magnetic and AB flux fields by the extended Nikiforov-Uvarov method

Applicability of the extended Nikiforov-Uvarov method in order to obtain eigenstate solutions of the radial Schrodinger equation in the presence of external magnetic field and Aharonov-Bohm (AB) flux fields is investigated. This study includes two analytical solutions of two different physical problems: solution of the non-relativistic wave equation for radial scalar power potential and solution for a charged particle with position-dependent mass interacted via Morse plus Coulomb potential under the influence of external magnetic field and AB flux fields. Wave function solutions for each case are achieved in terms of biconfluent Heun polynomials.