Quantum oscillator onCPnin a constant magnetic field

2004/06/22 by Stefano Bellucci, Armen Nersessian, Armen Yeranyan · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th

paper · pdf · doi:10.1103/physrevd.70.085013

published as Phys.Rev. D70 (2004) 085013 · 9 pages, 1 figure

arxiv created 2004/06/22 · openalex publication_date 2004/10/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces ℂP^N, as well as on their noncompact counterparts, i.e., the N-dimensional Lobachewski spaces L_N. 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 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 these results to the cones constructed over ℂP^N and L_N, and perform the Kustaanheimo-Stiefel transformation of these systems to the three dimensional Coulomb-like systems.

Citations

• Supersymmetric Kähler oscillator in a constant magnetic field

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