Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 23, 2014

Solution of the Dirac equation with magnetic monopole and pseudoscalar potentials

Sohrab Aghaei EMAIL logo and Alireza Chenaghlou
From the journal Open Physics

Abstract

The Dirac equation in the presence of the Dirac magnetic monopole potential, the Aharonov-Bohm potential, a Coulomb potential and a pseudo-scalar potential, is solved by separation of variables using the spinweighted spherical harmonics. The energy spectrum and the form of the spinor functions are obtained. It is shown that the number j in spin-weighted spherical harmonics must be greater than $$\left| q \right| - \tfrac{1} {2}$$.

[1] P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) http://dx.doi.org/10.1098/rspa.1931.013010.1098/rspa.1931.0130Search in Google Scholar

[2] S. R. Coleman, The magnetic monopole fifty years later, in: Les Houches Summer School, p. 461, 1981 Search in Google Scholar

[3] P. Goddard, D. I. Olive, Rep. Prog. Phys. 41, 1357 (1978) http://dx.doi.org/10.1088/0034-4885/41/9/00110.1088/0034-4885/41/9/001Search in Google Scholar

[4] R. Jackiw, Ann. Phys. 129, 183 (1980) http://dx.doi.org/10.1016/0003-4916(80)90295-X10.1016/0003-4916(80)90295-XSearch in Google Scholar

[5] Victor M. Villalba, J. Math. Phys. 36, 3332 (1995) http://dx.doi.org/10.1063/1.53103410.1063/1.531034Search in Google Scholar

[6] L. V. Hoang, L. X. L. I. Komarov, T. S. Romanova J. Phys A: Math. Gen 25, 6461 (1992) http://dx.doi.org/10.1088/0305-4470/25/23/03810.1088/0305-4470/25/23/038Search in Google Scholar

[7] A. D. Alhaidari, Phys. Lett. A 322, 72 (2004) http://dx.doi.org/10.1016/j.physleta.2004.01.00610.1016/j.physleta.2004.01.006Search in Google Scholar

[8] A. D. Alhaidari, Annals Phys. 320, 453 (2005), Erratum-ibid. 321, 1524 (2006) http://dx.doi.org/10.1016/j.aop.2005.07.00110.1016/j.aop.2005.07.001Search in Google Scholar

[9] A. D. Alhaidari, Found. Phys. Lett. 18, 651 (2005) http://dx.doi.org/10.1007/s10702-005-1318-x10.1007/s10702-005-1318-xSearch in Google Scholar

[10] V. G. Bagrov, D. M. Gitman, V. B. Tlyachev, J. Math. Phys. 42, 1933 (2001) http://dx.doi.org/10.1063/1.135318210.1063/1.1353182Search in Google Scholar

[11] W. J. Marciano, I. J. Muzinich, Phys. Rev. Lett. 50, 1035 (1983) http://dx.doi.org/10.1103/PhysRevLett.50.103510.1103/PhysRevLett.50.1035Search in Google Scholar

[12] E. T. Newman, R. Penrose, J. Math. Phys. 7, 863 (1966) http://dx.doi.org/10.1063/1.193122110.1063/1.1931221Search in Google Scholar

[13] Abhay G. Shah, John L. Friedman, Tobias S. Keidl, arXiv:1207.5595 [gr-qc] Search in Google Scholar

[14] Alan Kostelecky, Matthew Mewes, Phys. Rev. D 85, 096005 (2012) http://dx.doi.org/10.1103/PhysRevD.85.09600510.1103/PhysRevD.85.096005Search in Google Scholar

[15] G. F. Torres del Castillo, L. C. Cortes-Cuautli, J. Math. Phys. 38, 2996 (1997) http://dx.doi.org/10.1063/1.53202810.1063/1.532028Search in Google Scholar

[16] T. T. Wu, C. N. Yang, Nucl. Phys. B 107, 365 (1976) http://dx.doi.org/10.1016/0550-3213(76)90143-710.1016/0550-3213(76)90143-7Search in Google Scholar

[17] G. F. Torres del Castillo, Revista Mexicana de Fisica 43, 514 (1997) Search in Google Scholar

[18] U. Percoco, V. M. Villalba, Phys. Lett. A 140, 105 (1989) http://dx.doi.org/10.1016/0375-9601(89)90499-410.1016/0375-9601(89)90499-4Search in Google Scholar

[19] C. R. Hagen, Phys. Rev. Letters, 64, 503 (1990); Int. J. Mod. Phys. A 6, 3119 (1991) http://dx.doi.org/10.1103/PhysRevLett.64.503Search in Google Scholar

[20] C. R. Hagen, Phys. Rev. D 48, 5935 (1993) http://dx.doi.org/10.1103/PhysRevD.48.593510.1103/PhysRevD.48.5935Search in Google Scholar

[21] S. A. Voropaev, D. V. Galtsov, D. A. Spasov, Phys. Lett. B 267, 91 (1991) http://dx.doi.org/10.1016/0370-2693(91)90529-Y10.1016/0370-2693(91)90529-YSearch in Google Scholar

[22] F. A. B. Coutinho, Y. Nogami, J.F. Perez, Phys. Rev. A 46, 6052 (1992) http://dx.doi.org/10.1103/PhysRevA.46.605210.1103/PhysRevA.46.6052Search in Google Scholar PubMed

[23] F. A. B. Coutinho, Y. Nogami, J. F. Perez, J. Phys. A 27, 6539 (1994) http://dx.doi.org/10.1088/0305-4470/27/19/02410.1088/0305-4470/27/19/024Search in Google Scholar

[24] F. A. B. Coutinho, J. F. Perez, Phys. Rev. D 49, 2092 (1994) http://dx.doi.org/10.1103/PhysRevD.49.209210.1103/PhysRevD.49.2092Search in Google Scholar

[25] H. Falomir, P. A. G. Pisani, J. Phys. A 34, 4143 (2001) http://dx.doi.org/10.1088/0305-4470/34/19/31210.1088/0305-4470/34/19/312Search in Google Scholar

[26] V. G. Bagrov, D. M. Gitman, V. B. Tlyachev, J. Math. Phys. 42, 1933 (2001) http://dx.doi.org/10.1063/1.135318210.1063/1.1353182Search in Google Scholar

[27] V. R. Khalilov, Phys. Rev. A 71, 012105 (2005) http://dx.doi.org/10.1103/PhysRevA.71.01210510.1103/PhysRevA.71.012105Search in Google Scholar

[28] F. A. B. Coutinho, J. F. Perez, Phys. Rev. D 48, 932 (1993) http://dx.doi.org/10.1103/PhysRevD.48.93210.1103/PhysRevD.48.932Search in Google Scholar PubMed

[29] J. N. Goldberg, A. J. MacFarlane, E. T. Newman, F. Rohrlich, E. C. G. Sudarshan, J. Math. Phys. 8, 2155 (1967) http://dx.doi.org/10.1063/1.170513510.1063/1.1705135Search in Google Scholar

[30] G. F. Torres del Castillo, Revista Mexicana de Fisica 43, 527 (1997) Search in Google Scholar

[31] G. F. Torres del Castillo, Revista Mexicana de Fisica 39, (1993) Search in Google Scholar

[32] G. F. Torres del Castillo, Revista Mexicana de Fisica 32 (1993) Search in Google Scholar

[33] G. F. Torres del Castillo, Revista Mexicana de Fisica 38, 753 (1992) Search in Google Scholar

[34] G. F. Torres del Castillo, 3-D Spinors, Spin-Weighted Functions and their Applications, (Birkhauser, Boston, 2003) http://dx.doi.org/10.1007/978-0-8176-8146-310.1007/978-0-8176-8146-3Search in Google Scholar

[35] G. V. Shishkin, V. M. Villalba, J. Math. Phys. 34, 5037 (1993) http://dx.doi.org/10.1063/1.53034010.1063/1.530340Search in Google Scholar

[36] A. S. Davydov, Quantum Mechanics (Pergamon, Oxford, 1965) Search in Google Scholar

Published Online: 2014-4-23
Published in Print: 2014-4-1

© 2014 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 1.12.2022 from frontend.live.degruyter.dgbricks.com/document/doi/10.2478/s11534-014-0447-x/html
Scroll Up Arrow