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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.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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[1] Alhaidari, A.D.: Solution of the relativistic Dirac-Morse problem. Phys. Rev. Lett. 87, 210405–21408 (2001) · doi:10.1103/PhysRevLett.87.210405
[2] Alhaidari, A.D.: Relativistic shape invariant potentials. J. Phys. A: Math. Gen. 35, 6207–6216 (2002) · Zbl 1066.81626 · doi:10.1088/0305-4470/35/29/501
[3] Cooper, F., Khare, A., Sukhatme, U.: Supersymmetry and quantum mechanics. Phys. Rep. 251, 267–385 (1995) · Zbl 0988.81001 · doi:10.1016/0370-1573(94)00080-M
[4] Dabrowska, J., Khare, A., Sukhatme, U.: Explicit wavefunctions for shape invariant potentials by operator technique. J. Phys. A: Math. Gen. 21, L195–L200 (1988) · doi:10.1088/0305-4470/21/4/002
[5] Dutt, R., Khare, A., Sukhatme, U.: Supersymmetry, shape invariance and exactly solvable potentials. Am. J. Phys. 56, 163 (1988) · doi:10.1119/1.15697
[6] Gang, C.: Solution of the Dirac equation with four-parameter diatomic potentials. Phys. Lett. A 328, 116–122 (2004) · Zbl 1134.81355 · doi:10.1016/j.physleta.2004.06.026
[7] Greiner, W.: Relativistic Quantum Mechanics. Springer, Berlin (1981)
[8] Jafarizadeh, M.A., Fakhri, H.: Supersymmetry and shape invariance in differential equations of mathematical physics. Phys. Lett. A 230, 164–170 (1997) · Zbl 1052.81524 · doi:10.1016/S0375-9601(97)00161-8
[9] Jafarizadeh, M.A., Fakhri, H.: Parasupersymmetry and shape invariance in differential equations of mathematical physics and quantum mechanics. Ann. Phys. 262, 260–276 (1998) · Zbl 0940.81022 · doi:10.1006/aphy.1997.5745
[10] Moshinsky, M., Szczepaniank, A.: The Dirac oscillator. J. Phys. A: Math. Gen. 22, L817–L819 (1989) · doi:10.1088/0305-4470/22/17/002
[11] Rodrigues, R.: Generalized ladder operators for the Dirac-Coulomb problem via SUSY QM. Phys. Lett. A 326, 42–46 (2004) · Zbl 1161.81374 · doi:10.1016/j.physleta.2004.04.013
[12] Zhao, X.Q., Jia, C.S., Yang, Q.B.: Bound states of relativistic particles in the generalized symmetrical double-well potential. Phys. Lett. A 337, 189–196 (2005) · Zbl 1135.81335
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