Heun functions and the energy spectrum of a charged particle on a sphere under a magnetic field and Coulomb force
Arnaud Ralko, T T Truong · Journal of Physics A Mathematical and General · 2002
We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: the magnetic length l B , the Bohr radius l 0 , and the radius of the sphere R . The energy spectrum of the particle is found by solving a Schrödinger equation of the Heun type, using the technique of continued fractions. This displays a rich set of functioning regimes where ratios R / l B and R / l 0 take definite values.