Regular Article - Theoretical Physics
A model of the two-dimensional quantum harmonic oscillator in an background
Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937, Cologne, Germany
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Accepted: 15 September 2016
Published online: 8 October 2016
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schrödinger picture in which the analogs of the Schrödinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations.
© The Author(s), 2016