How to relate the oscillator and Coulomb systems on spheres and pseudospheres?

Details How to relate the oscillator and Coulomb systems on spheres and pseudospheres? How to relate the oscillator and Coulomb systems on spheres and pseudospheres?

2000-10-29

arxiv.org/abs/math-ph/0010049v1

Phys.Atom.Nucl.65:1070-1075,2002; Yad.Fiz.65:1103-1108,2002

Physics

Mathematical Physics

12 pages, Based on talk given at XXIII Colloquium on Group Theoretical Methods in Physics (July 31-August 5, 2000, Dubna)

Scientific paper

10.1134/1.1490113

We show that the oscillators on a sphere and pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere: the even states of an oscillator yields the conventional Coulomb system on pseudosphere, while the odd states yield the Coulomb system on pseudosphere in the presence of magnetic flux tube generating half spin. In the higher dimensions the oscillator and Coulomb(-like) systems are connected in the similar way. In particular, applying the Kustaanheimo-Stiefel transformation to the oscillators on sphere and pseudosphere, we obtained the preudospherical generalization of MIC-Kepler problem describing three-dimensional charge-dyon system.

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