Exact energy levels and eigenfunctions of an electron on a nanosphere under the influence of a radial magnetic field

Abstract

The exact energy levels and wave functions of an electron that is free to move on a nanosphere under the influence of a radial magnetic field have been determined. The wave functions are expressed in terms of Jacobi polynomials that are well defined and orthogonal and can be expressed using recurrence relations and series expansions. We also discuss the wave functions and energy levels in the presence of a very high magnetic field. Landau energy levels are shown for strong constant magnetic fields occurring on two-dimensional flat surfaces, if the radius is very large. The results are compared with those of previously published researches.