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

Panahi, H.; Jahangiry, L.

Int. J. Theor. Phys. 48, No. 11, 3234-3240 (2009).

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.

MSC:

81Q05

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

Keywords:

Dirac-shifted oscillator; Dirac-Morse; Rodrigues representation; shape invariance

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