Quantum Oscillator on $\DC P^n$ in a constant magnetic field

Details Quantum Oscillator on $\DC P^n$ in a constant magnetic field Quantum Oscillator on $\DC P^n$ in a constant magnetic field

2004-06-22

arxiv.org/abs/hep-th/0406184v1

Phys.Rev. D70 (2004) 085013

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, 1 figure

Scientific paper

10.1103/PhysRevD.70.085013

We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces $\DC P^N$, as well as on their non-compact counterparts, i. e. the $N-$dimensional Lobachewski spaces ${\cal L}_N$. We find the spectrum of this system and the complete basis of wavefunctions. Surprisingly, the inclusion of a magnetic field does not yield any qualitative change in the energy spectrum. For $N>1$ the magnetic field does not break the superintegrability of the system, whereas for N=1 it preserves the exact solvability of the system. We extend this results to the cones constructed over $\DC P^N$ and ${\cal L}_N$, and perform the (Kustaanheimo-Stiefel) transformation of these systems to the three-dimensional Coulomb-like systems.

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