Shape invariant and Rodrigues solution of the Dirac-shifted oscillator and Dirac-Morse potentials. (English) Zbl 1184.81051

Summary: We show that the Dirac equation for a charged spinor in spherically symmetric electromagnetic potentials as Dirac-shifted oscillator and Dirac-Morse potentials have the conditions of shape invariant symmetry in non-relativistic quantum mechanics. The relativistic spectra of the bound states and spinor wavefunctions can be obtained by the Rodrigues polynomials of one associated differential equation.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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