Quantum oscillator on CPn in a constant magnetic field

Stefano Bellucci, Armen Nersessian, and Armen Yeranyan
Phys. Rev. D 70, 085013 – Published 15 October 2004

Abstract

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

  • Figure
  • Received 25 June 2004

DOI:https://doi.org/10.1103/PhysRevD.70.085013

©2004 American Physical Society

Authors & Affiliations

Stefano Bellucci1, Armen Nersessian2,3, and Armen Yeranyan2

  • 1INFN-Laboratori Nazionali di Frascati, P.O. Box 13, I-00044, Frascati, Italy
  • 2Yerevan State University, Alex Manoogian St., 1, Yerevan, 375025, Armenia
  • 3Yerevan Physics Institute, Alikhanian Brothers St., 2, Yerevan, 375036, Armenia

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Issue

Vol. 70, Iss. 8 — 15 October 2004

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