Geometric Models of the Relativistic Harmonic Oscillator

  title={Geometric Models of the Relativistic Harmonic Oscillator},
  author={Ion I. Cot{\`u}aescu},
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.