Abstract
We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces , as well as on their noncompact counterparts, i.e., the -dimensional Lobachewski spaces . We find the spectrum of this system and the complete basis of wave functions. Surprisingly, the inclusion of a magnetic field does not yield any qualitative change in the energy spectrum. For the magnetic field does not break the superintegrability of the system, whereas for it preserves the exact solvability of the system. We extend these results to the cones constructed over and , and perform the Kustaanheimo-Stiefel transformation of these systems to the three dimensional Coulomb-like systems.
- Received 25 June 2004
DOI:https://doi.org/10.1103/PhysRevD.70.085013
©2004 American Physical Society