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Dirac equation in presence of the Hartmann and Higgs oscillator superintegrable potentials with the spin and pseudospin symmetries

V. Mohammadi

Department of Physics, Faculty of Science, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran

E-mail Address: v.mohammadi@sut.ac.ir

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S. Aghaei

Department of Physics, Faculty of Science, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran

E-mail Address: so_aghaei@sut.ac.ir

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, and

A. Chenaghlou

Department of Physics, Faculty of Science, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran

E-mail Address: a.chenaghlou@sut.ac.ir

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https://doi.org/10.1142/S0217751X16501906Cited by:11 (Source: Crossref)

Abstract

The spin and pseudospin symmetries in the Dirac Hamiltonian are investigated in the presence of the Hartmann and the Higgs oscillator superintegrable potentials. The Pauli-Dirac representation is used in the Dirac equation with scalar and vector potentials of equal magnitude. Then, the Dirac equation is reduced to a Schrödinger-like equation. The symmetry algebras of the Schrödinger-like equation corresponding to the superintegrable potentials are represented. Also, the associated irreducible representations are shown by means of the quadratic algebras. Finally, the relativistic energy spectra of the Hartmann and the Higgs oscillator superintegrable potentials are calculated.

Keywords:

PACS: 03.65.Pm, 03.65.-w, 03.65.Fd, 02.30.Ik

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References

1. G. Smith and L. Tassie, Ann. Phys. 65, 352 (1971). Crossref, Web of Science, ADS, Google Scholar
2. J. Bell and H. Ruegg, Nucl. Phys. B 98, 151 (1975). Crossref, Web of Science, ADS, Google Scholar
3. G. Eyre and H. Osborn, Nucl. Phys. B 116, 281 (1976). Crossref, Web of Science, ADS, Google Scholar
4. A. Arima, M. Harvey and K. Shimizu, Phys. Lett. B 30, 517 (1969). Crossref, Web of Science, ADS, Google Scholar
5. K. Hecht and A. Adler, Nucl. Phys. A 137, 129 (1969). Crossref, Web of Science, ADS, Google Scholar
6. D. Troltenier, C. Bahri and J. Draayer, Nucl. Phys. A 586, 53 (1995). Crossref, Web of Science, ADS, Google Scholar
7. J. Dudek, W. Nazarewicz, Z. Szymanski and G. Leander, Phys. Rev. Lett. 59, 1405 (1987). Crossref, Web of Science, ADS, Google Scholar
8. Å. Bohr, I. Hamamoto and B. R. Mottelson, Phys. Scr. 26, 267 (1982). Crossref, Web of Science, ADS, Google Scholar
9. W. Nazarewicz, P. Twin, P. Fallon and J. Garrett, Phys. Rev. Lett. 64, 1654 (1990). Crossref, Web of Science, ADS, Google Scholar
10. B. Mottelson, Nucl. Phys. A 522, 1 (1991). Crossref, ADS, Google Scholar
11. J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997). Crossref, Web of Science, ADS, Google Scholar
12. J. N. Ginocchio and D. G. Madland, Phys. Rev. C 57, 1167 (1998). Crossref, Web of Science, ADS, Google Scholar
13. J. N. Ginocchio, Phys. Rev. Lett. 95, 252501 (2005). Crossref, Web of Science, ADS, Google Scholar
14. J. N. Ginocchio, Phys. Rep. 414, 165 (2005). Crossref, Web of Science, ADS, Google Scholar
15. F.-L. Zhang and J.-L. Chen, J. Math. Phys. 50, 032301 (2009). Crossref, Web of Science, Google Scholar
16. E. G. Kalnins, J. A. Kress and W. Miller Jr., J. Math. Phys. 47, 043514 (2006). Crossref, Web of Science, Google Scholar
17. E. G. Kalnins, J. A. Kress and W. Miller Jr., J. Math. Phys. 46, 103507 (2005). Crossref, Web of Science, ADS, Google Scholar
18. E. G. Kalnins, J. M. Kress and W. Miller Jr, J. Math. Phys. 46, 053509 (2005). Crossref, Web of Science, ADS, Google Scholar
19. E. G. Kalnins, W. Miller Jr. and G. Pogosyan, J. Math. Phys. 37, 6439 (1996). Crossref, Web of Science, ADS, Google Scholar
20. E. G. Kalnins, W. Miller Jr. and G. Pogosyan, J. Phys. A: Math. Gen. 33, 4105 (2000). Crossref, ADS, Google Scholar
21. E. G. Kalnins, J. Kress, G. Pogosyan and W. Miller Jr., J. Phys. A: Math. Gen. 34, 4705 (2001). Crossref, ADS, Google Scholar
22. S. Gravel and P. Winternitz, J. Math. Phys. 43, 5902 (2002). Crossref, Web of Science, ADS, Google Scholar
23. I. Marquette, J. Phys. A: Math. Theor. 43, 135203 (2010). Crossref, Web of Science, ADS, Google Scholar
24. I. Marquette and P. Winternitz, J. Phys. A: Math. Theor. 41, 304031 (2008). Crossref, Web of Science, Google Scholar
25. S. Post, SIGMA 7, 036 (2011). Google Scholar
26. P. Winternitz, Y. A. Smorodinsky, M. Uglirzh and I. Frish, Yad. Fiz. 4, 625 (1966). Google Scholar
27. C. Daskaloyannis, J. Math. Phys. 42, 1100 (2001). Crossref, Web of Science, ADS, Google Scholar
28. C. Quesne, SIGMA 3, 14 (2007). Google Scholar
29. Y. I. Granovskii, A. S. Zhedanov and I. Lutzenko, J. Phys. A: Math. Gen. 24, 3887 (1991). Crossref, ADS, Google Scholar
30. Y. I. Granovskii, A. S. Zhedanov and I. Lutsenko, Theor. Math. Phys. 91, 474 (1992). Crossref, Web of Science, Google Scholar
31. Y. I. Granovskii, A. S. Zhedanov and I. Lutsenko, Theor. Math. Phys. 91, 604 (1992). Crossref, Web of Science, Google Scholar
32. D. Bonatsos, C. Daskaloyannis and K. Kokkotas, Phys. Rev. A 50, 3700 (1994). Crossref, Web of Science, ADS, Google Scholar
33. E. G. Kalnins, J. M. Kress, W. Miller Jr. and S. Post, SIGMA 5, 8 (2009). Google Scholar
34. C. Daskaloyannis and Y. Tanoudis, Phys. Atom. Nucl. 73, 214 (2010). Crossref, Web of Science, ADS, Google Scholar
35. I. Marquette, J. Phys. A: Math. Theor. 44, 235203 (2011). Crossref, Web of Science, ADS, Google Scholar
36. S. Aghaei and A. Chenaghlou, Few-Body Syst. 56, 53 (2015). Crossref, Web of Science, ADS, Google Scholar
37. H. Hartmann, Theor. Chim. Acta 24, 201 (1972). Crossref, Google Scholar
38. M. Kibler and T. Negadi, Int. J. Quantum Chem. 26, 405 (1984). Crossref, Web of Science, Google Scholar
39. H. Hartmann, R. Schuck and J. Radtke, Theor. Chim. Acta 42, 1 (1976). Crossref, Google Scholar
40. C. C. Gerry, Phys. Lett. A 118, 445 (1986). Crossref, Web of Science, ADS, Google Scholar
41. G. G. Blado, Int. J. Quantum Chem. 58, 431 (1996). Crossref, Web of Science, Google Scholar
42. I. Sökmen, Phys. Lett. A 115, 249 (1986). Crossref, Web of Science, ADS, Google Scholar
43. Q. Shang-Wu, H. Bo-Wen, W. De-Yun and G. Zhi-Yu, Commun. Theor. Phys. 38, 139 (2002). Crossref, ADS, Google Scholar
44. A. N. Vaidya and H. Boschi Filho, J. Math. Phys. 31, 1951 (1990). Crossref, Web of Science, ADS, Google Scholar
45. M. Kibler and P. Winternitz, J. Phys. A: Math. Gen. 20, 4097 (1987). Crossref, ADS, Google Scholar
46. C.-Y. Chen, C.-L. Liu and D.-S. Sun, Phys. Lett. A 305, 341 (2002). Crossref, Web of Science, ADS, Google Scholar
47. C.-Y. Chen, F.-L. Lu and D.-S. Sun, Phys. Lett. A 329, 420 (2004). Crossref, Web of Science, ADS, Google Scholar
48. C.-Y. Chen, D.-S. Sun and C.-L. Liu, Phys. Lett. A 317, 80 (2003). Crossref, Web of Science, ADS, Google Scholar
49. P. W. Higgs, J. Phys. A: Math. Gen. 12, 309 (1979). Crossref, ADS, Google Scholar
50. M. Ikeda and N. Katayama, Tensor NS 38, 37 (1982). Google Scholar
51. E. Kalnins, W. Miller Jr. and S. Post, J. Phys. A: Math. Theor. 40, 11525 (2007). Crossref, Web of Science, ADS, Google Scholar
52. E. G. Kalnins, W. Miller Jr. and S. Post, SIGMA 9, 057 (2013). Google Scholar
53. S. Gao, Y. Wang and B. Hou, Linear Alg. Appl. 439, 1834 (2013). Crossref, Web of Science, Google Scholar
54. Y. I. Granovskii, I. Lutzenko and A. Zhedanov, Ann. Phys. 217, 1 (1992). Crossref, Web of Science, ADS, Google Scholar
55. P. Terwilliger, SIGMA 7, 26 (2011). Google Scholar
56. A. de Souza Dutra and M. Hott, Phys. Lett. A 356, 215 (2006). Crossref, Web of Science, ADS, Google Scholar
57. A. Alhaidari, H. Bahlouli and A. Al-Hasan, Phys. Lett. A 349, 87 (2006). Crossref, Web of Science, ADS, Google Scholar
58. J. N. Ginocchio, Phys. Rev. C 69, 034318 (2004). Crossref, Web of Science, ADS, Google Scholar
59. F.-L. Zhang, B. Fu and J.-L. Chen, Phys. Rev. A 78, 040101 (2008). Crossref, Web of Science, ADS, Google Scholar
60. V. Mohammadi, S. Aghaei and A. Chenaghlou, Adv. High Energy Phys. 2015, 701042 (2015). Crossref, Web of Science, Google Scholar
61. C. Berkdemir and Y.-F. Cheng, Phys. Scr. 79, 035003 (2009). Crossref, Web of Science, Google Scholar
62. M.-C. Zhang, G.-Q. Huang-Fu and B. An, Phys. Scr. 80, 5018 (2009). Google Scholar
63. Y. Zhou and J.-Y. Guo, Chin. Phys. B 17, 380 (2008). Crossref, Web of Science, ADS, Google Scholar
64. J. Guo-Xing and R. Zhong-Zhou, Commun. Theor. Phys. 49, 319 (2008). Crossref, Web of Science, Google Scholar
65. G. Chen, Z.-D. Chen and Z.-M. Lou, Phys. Lett. A 331, 374 (2004). Crossref, Web of Science, ADS, Google Scholar
66. G. Chen, Z.-D. Chen and P.-C. Xuan, Phys. Lett. A 352, 317 (2006). Crossref, Web of Science, ADS, Google Scholar
67. R. L. Hall and Ö. Yeşiltaş, Int. J. Mod. Phys. E 19, 1923 (2010). Link, ADS, Google Scholar
68. I. Marquette, J. Math. Phys. 52, 042301 (2011). Crossref, Web of Science, Google Scholar
69. S. Aghaei and A. Chenaghlou, Int. J. Mod. Phys. A 29, 1450028 (2014). Link, Web of Science, ADS, Google Scholar
70. F. Yaşuk, C. Berkdemir and A. Berkdemir, J. Phys. A: Math. Gen. 38, 6579 (2005). Crossref, ADS, Google Scholar