Bound states of the Dirac equation with vector and scalar Scarf-type potentials. (English) Zbl 1145.81363
Summary: Solving the Dirac equations with equal Scarf-type scalar and vector potentials by the method of the supersymmetric quantum mechanics, shape invariance approach and the alternative method, we obtain the exact energy equations and unnormalized wavefunctions for the s-wave bound states. Some interesting results including the standard Scarf II, generalized Pöschl-Teller and Pöschl-Teller II potentials are also discussed.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
References:
| [1] | Wang, I. C.; Wong, C. Y., Phys. Rev. D, 34, 348 (1988) |
| [2] | Domínguez-Adame, F., Phys. Lett. A, 136, 175 (1989) |
| [3] | Domínguez-Adame, F.; Rodríguez, A., Phys. Lett. A, 198, 275 (1995) |
| [4] | Rao, N. A.; Kagali, B. A., Phys. Lett. A, 296, 192 (2002) · Zbl 0994.81031 |
| [5] | Villalba, V. M.; Isasi, E., J. Math. Phys., 43, 4909 (2002) |
| [6] | Dong, S. H.; Lozada-Cassou, M., Phys. Lett. A, 330, 168 (2004) · Zbl 1209.81179 |
| [7] | Samsonov, B. F.; Pecheritsin, A. A.; Pozdeeva, E. O.; Glasser, M. L., Eur. J. Phys., 24, 435 (2003) · Zbl 1038.81017 |
| [8] | Mustafa, O., Czech. J. Phys., 54, 529 (2004) |
| [9] | Alhaidari, A. D., Phys. Lett. A, 326, 58 (2004) · Zbl 1161.81338 |
| [10] | Simsek, M.; Egrifes, H., J. Phys. A: Math. Gen., 37, 4379 (2004) · Zbl 1053.81023 |
| [11] | Su, R. K.; Ma, Z. Q., J. Phys. A: Math. Gen., 19, 1739 (1986) · Zbl 0617.35125 |
| [12] | Qiang, W. C., Chin. Phys., 12, 136 (2003) |
| [13] | Qiang, W. C., Chin. Phys., 13, 575 (2004) |
| [14] | Chen, G.; Chen, Z. D.; Lou, Z. M., Chin. Phys., 13, 279 (2004) |
| [15] | Zhang, X. A.; Chen, K.; Duan, Z. L., Chin. Phys., 14, 42 (2005) |
| [16] | Diao, Y. F.; Yi, L. Z.; Jia, C. S., Phys. Lett. A, 332, 157 (2004) · Zbl 1123.35343 |
| [17] | Yi, L. Z.; Diao, Y. F.; Liu, J. Y.; Jia, C. S., Phys. Lett. A, 333, 212 (2004) · Zbl 1123.81350 |
| [18] | Zhao, X. Q.; Jia, C. S.; Yang, Q. B., Phys. Lett. A, 337, 189 (2005) · Zbl 1135.81335 |
| [19] | Beavis, D.; Chu, S. Y.; Desai, B. R.; Kaus, P., Phys. Rev. D, 20, 2345 (1979) |
| [20] | Fishbane, P. M.; Gasiorowicz, S. G.; Johannsen, D. C.; Kaus, P., Phys. Rev. D, 27, 2433 (1983) |
| [21] | Sukumar, C. V., J. Phys. A: Math. Gen., 18, 2917 (1985) |
| [22] | Gendenshtein, L. E., Sov. Phys. JETP Lett., 38, 356 (1983) |
| [23] | Cooper, F.; Khare, A.; Sukhatme, U., Phys. Rep., 251, 267 (1995) |
| [24] | Eğrifes, H.; Demirhan, D.; Büyükkılıç, F., Phys. Lett. A, 275, 229 (2000) · Zbl 1115.81332 |
| [25] | Arai, A., J. Math. Anal. Appl., 158, 63 (1991) · Zbl 0731.47055 |
| [26] | Jia, C. S.; Li, Y.; Sun, Y.; Liu, J. Y.; Sun, L. T., Phys. Lett. A, 311, 115 (2003) · Zbl 1059.81046 |
| [27] | Jia, C. S.; Sun, Y.; Li, Y., Phys. Lett. A, 305, 231 (2002) · Zbl 1001.81018 |
| [28] | Qian, S. W.; Huang, B. W.; Wang, D. Y.; Gu, Z. Y., Commun. Theor. Phys., 38, 139 (2002) · Zbl 1267.81175 |
| [29] | Zeng, J. Y., Quantum Mechanics, vol. II (1990), Science Press: Science Press Beijing, (in Chinese) |
| [30] | De, R.; Dutt, R.; Sukhatme, U., J. Phys. A: Math. Gen., 25, L843 (1992) |
| [31] | Dabrowska, J. W.; Khare, A.; Sukhatme, U. P., J. Phys. A: Math. Gen., 21, L195 (1988) |
| [32] | Jia, C. S.; Wang, X. G.; Yao, X. K.; Chen, P. C.; Xiao, W., J. Phys. A: Math. Gen., 31, 4763 (1998) · Zbl 0931.34070 |
| [33] | Fakhri, H.; Chenaghlou, A., J. Phys. A: Math. Gen., 37, 8545 (2004) · Zbl 1064.81050 |
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.
