Confined Dirac Electron in Coulomb and Uniform Magnatic Fields: The Hill Determinant Approach

Abstract

The 2+1 dimensional Dirac equation is solved for electron in an oscillator potential together with external fields. Approximate eigenenergies are determined from a second order recurrence relation using the Hill determinant technique. In addition, the technique is shown to generate wave functions for the quasi-exactly solvable problem. Finite analytic closed form for the recurrence relation derived using the recursive-sum plus discrete dimensional-convolution techniques is shown to be in agreement with the analytic result from the finite Hill determinant.