Solution and hidden supersymmetry of a Dirac oscillator. (English) Zbl 1050.81524

Benítez, J.; Martínez y Romero, R. P.; Núñez Yépez, H. N.; Salas-Brito, A. L.

Phys. Rev. Lett. 64, No. 14, 1643-1645 (1990); errata ibid. 65, No. 16, 2085 (1990).

Summary: 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.

MSC:

81Q05

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

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