×

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials. (English) Zbl 1045.81021

Summary: The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrödinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Landau, L. D.; Lifshitz, E. M., Quantum Mechanics (1958), Pergamon: Pergamon New York · Zbl 0081.22207
[2] Gol’dman, I. I.; Krivchenkov, V. D., Problems in Quantum Mechanics (1961), Pergamon: Pergamon London · Zbl 0094.23407
[3] Peak, D.; Inomata, A., J. Math. Phys., 10, 1422 (1969)
[4] Constantinescu, F.; Magyari, E., Problems in Quantum Mechanics (1971), Pergamon: Pergamon Oxford
[5] Bagrov, V. G.; Gitman, D. M., Exact Solutions of Relativistic Wave Equations (1990), Kluwer: Kluwer Dordrecht · Zbl 0723.35066
[6] Pama, G.; Raff, U., Am. J. Phys., 71, 247 (2003)
[7] Calogero, F., J. Math. Phys., 10, 2191 (1969)
[8] Calogero, F., J. Math. Phys., 12, 419 (1971)
[9] Hall, R. L.; Saad, N.; von Keviczky, A., J. Math. Phys., 39, 6345 (1998) · Zbl 0935.81015
[10] Hall, R. L.; Saad, N., J. Phys. A, 33, 5531 (2000)
[11] Hall, R. L.; Saad, N., J. Phys. A, 33, 569 (2000) · Zbl 1002.81011
[12] Hall, R. L.; Saad, N., J. Phys. A, 34, 1169 (2001)
[13] Hall, R. L.; Saad, N.; von Keviczky, A., J. Math. Phys., 43, 94 (2002) · Zbl 1059.81044
[14] Hall, R. L.; Saad, N.; von Keviczky, A., J. Phys. A, 36, 487 (2003) · Zbl 1047.81027
[15] Nagiyev, S. M.; Jafarov, E. I.; Imanov, R. M., J. Phys. A, 36, 7813 (2003) · Zbl 1062.70039
[16] Camiz, P.; Gerardi, A.; Marchioro, C.; Presutti, E.; Scacciatelli, E., J. Math. Phys., 12, 2040 (1971) · Zbl 0224.35081
[17] Dodonov, V. V.; Malkin, I. A.; Man’ko, V. I., Phys. Lett. A, 39, 377 (1972)
[18] de Castro, A. S., Phys. Lett. A, 318, 40 (2003) · Zbl 1098.81772
[19] Strange, P., Relativistic Quantum Mechanics (1998), Cambridge University Press: Cambridge University Press Cambridge
[20] de Castro, A. S.; Pereira, W. G., Phys. Lett. A, 308, 131 (2003) · Zbl 1008.81020
[21] de Castro, A. S., Phys. Lett. A, 309, 340 (2003) · Zbl 1011.81509
[22] Moshinsky, M.; Szczepaniak, A., J. Phys. A, 22, L817 (1989)
[23] Nogami, Y.; Toyama, F. M., Can. J. Phys., 74, 114 (1996)
[24] Toyama, F. M.; Nogami, Y.; Coutinho, F. A.B., J. Phys. A, 30, 2585 (1997) · Zbl 0924.35120
[25] Toyama, F. M.; Nogami, Y., Phys. Rev. A, 59, 1056 (1999)
[26] Szmytkowski, R.; Gruchowski, M., J. Phys. A, 34, 4991 (2001) · Zbl 0983.81012
[27] Pacheco, M. H.; Landim, R.; Almeida, C. A.S., Phys. Lett. A, 311, 93 (2003) · Zbl 1038.82058
[28] Thaller, B., The Dirac Equation (1992), Springer: Springer Berlin · Zbl 0881.47021
[29] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1965), Dover: Dover Toronto · Zbl 0515.33001
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.