×

Dirac equation exact solutions for generalized asymmetrical Hartmann potentials. (English) Zbl 1160.35514

Summary: In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar potential. The cases of some quasi-exactly solvable and Morse-like potentials are briefly commented.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Chen, C.Y., Phys. lett. A, 339, 283, (2005)
[2] Hartmann, H., Theor. chim. acta, 24, 201, (1972)
[3] Chen, C.Y.; Liu, C.L.; Sun, D.S., Phys. lett. A, 305, 341, (2002)
[4] Chen, C.Y.; Sun, D.S.; Liu, C.L., Phys. lett. A, 317, 80, (2003)
[5] Chen, C.Y.; Lu, F.L.; Sun, D.S., Phys. lett. A, 329, 420, (2004)
[6] Chen, C.Y.; Dong, S.H., Phys. lett. A, 335, 374, (2005)
[7] Hautot, A., J. math. phys., 14, 1320, (1973)
[8] Flessas, G.P.; Das, K., Phys. lett. A, 78, 19, (1980)
[9] de Souza Dutra, A., Phys. lett. A, 131, 319, (1988)
[10] Alhaidari, A.D.; Alhaidari, A.D.; Alhaidari, A.D., Phys. rev. lett., Phys. rev. lett., J. phys. A, 34, 9827, (2002) · Zbl 1059.81172
[11] Vaidya, A.N.; Rodrigues, R.L., Phys. rev. lett., 89, 068901, (2002)
[12] de Castro, A.S., J. phys. A, 35, 6203, (2002)
[13] Landau, L.D.; Lifshitz, E.M., Quantum mechanics, (1958), Pergamon Elmsford, NY · Zbl 0081.22207
[14] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1965), Dover Toronto · Zbl 0515.33001
[15] Ushveridze, A.G., Quasi-exactly solvable models in quantum mechanics, (1994), Institute of Physics Bristol · Zbl 0834.58042
[16] de Souza Dutra, A.; de Castro, A.S.; da Silva, E.A.; Castilho, L.C.O., J. phys. A, 36, 1711, (2003) · Zbl 1070.81111
[17] Morse, P.M., Phys. rev., 34, 57, (1929)
[18] Flügge, S., Practical quantum mechanics, (1979), Springer-Verlag Berlin
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.