Relation of the oscillator and Coulomb systems on spheres and pseudospheres

Details Relation of the oscillator and Coulomb systems on spheres and pseudospheres Relation of the oscillator and Coulomb systems on spheres and pseudospheres

2000-06-26

arxiv.org/abs/quant-ph/0006118v3

Phys.Rev.A63:020103,2001

Physics

Quantum Physics

4pp, revised version: title changed, misprints corrected, two references added

Scientific paper

10.1103/PhysRevA.63.020103

It is shown, that oscillators on the sphere and the pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere. The even states of an oscillator yield the conventional Coulomb system on the pseudosphere, while the odd states yield the Coulomb system on the pseudosphere in the presence of magnetic flux tube generating spin 1/2. A similar relation is established for the oscillator on the (pseudo)sphere specified by the presence of constant uniform magnetic field $B_0$ and the Coulomb-like system on pseudosphere specified by the presence of the magnetic field $\frac{B}{2r_0}(|\frac{x_3}{{\bf x}}|-\epsilon)$. The correspondence between the oscillator and the Coulomb systems the higher dimensions is also discussed.

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