Solution and hidden supersymmetry of a Dirac oscillator

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Abstract
In this paper we found, by explicitly solving the Dirac equation, the complete energy spectrum and the corresponding eigenfunctions, for both the positive- and the negative-energy states, of the recently proposed Dirac oscillator. We found the electromagnetic potential associated with its interaction term. This exactly soluble problem has a hidden supersymmetry responsible for the special properties of its energy spectrum. We discuss the implications of this supersymmetry in the stability of the Dirac sea and we calculate the related superpotential.