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

Abstract

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 ${\mathcal{L}}_N$. 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 ${\mathcal{L}}_N$, and perform the (Kustaanheimo-Stiefel) transformation of these systems to the three-dimensional Coulomb-like systems.

9 pages, 1 figure

References in corpus (1)

• Supersymmetric Kähler oscillator in a constant magnetic field

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