A (1+3) Relativistic Harmonic Oscillator Simulated by an Anti-de Sitter   Background
  It is shown that a static $(1+3)$ anti-de Sitter metric defines, in a natural way, a relativistic harmonic oscillator in Minkowski space. The quantum theory can be solved exactly and leads to wave functions having a significantly different behaviour with respect to the non-relativistic ones. The energy spectrum coincides, up to the ground state energy, with that of the non-relativistic oscillator. 
D. J. Navarro and J. Navarro-Salas