Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

Details Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

2002-09-27

arxiv.org/abs/quant-ph/0209152v1

Physics

Quantum Physics

12 pages, 5 figures, accepted to JOPA, november 2002

Scientific paper

10.1088/0305-4470/35/45/306

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: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.

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