Geometric Models of the Relativistic Harmonic Oscillator

Details Geometric Models of the Relativistic Harmonic Oscillator Geometric Models of the Relativistic Harmonic Oscillator

1997-04-10

arxiv.org/abs/physics/9704009v1

Int.J.Mod.Phys. A12 (1997) 3545-3550

Physics

Mathematical Physics

8 pages, Latex

Scientific paper

10.1142/S0217751X97001833

A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.

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