×

\((1+1)\)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: Effectively \(\mathcal{PT}\)-symmetric. (English) Zbl 1140.81363

Summary: The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the \((1+1)\)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the “quasi-parity” on the Dirac particles’ spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form \(S (z)= S (x - ib)\) (an inversely linear plus linear, leading to a \(\mathcal{PT-}\) symmetric oscillator model), and \(S (x)= S_{r}(x)+ iS_{i}(x) (a \mathcal{PT}\) -symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an \(\eta\)-weak-pseudo-Hermiticity generator are presented and a complexified \(\mathcal{PT}\) -symmetric periodic-type model is used as an illustrative example.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q60 Supersymmetry and quantum mechanics
78A35 Motion of charged particles
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Nogami, N., Toyama, F.M.: Phys. Rev. A 47, 1708 (1993) · doi:10.1103/PhysRevA.47.1708
[2] Nogami, N., Toyama, F.M.: Phys. Rev. A 57, 93 (1998) · doi:10.1103/PhysRevA.57.93
[3] Witten, E.: Nucl. Phys. B 188, 513 (1981) · Zbl 1258.81046 · doi:10.1016/0550-3213(81)90006-7
[4] Cooper, F., Khare, A., Sukhatme, U.: Phys. Rep. 251, 267 (1995) · doi:10.1016/0370-1573(94)00080-M
[5] Sukumar, C.V.: J. Phys. A: Math. Gen. 18, 2917 (1985) · doi:10.1088/0305-4470/18/15/020
[6] Cooper, F., et al.: Ann. Phys. 187, 1 (1987)
[7] de Castro, A.S., Hott, M.: Phys. Lett. A 342, 53 (2005) · Zbl 1222.81171 · doi:10.1016/j.physleta.2005.05.039
[8] Sinha, A., Roy, P.: Mod. Phys. Lett. A 20, 2377 (2005) · Zbl 1081.81036 · doi:10.1142/S0217732305017664
[9] Jackiw, R., Rebbi, C.: Phys. Rev. D 13, 3398 (1976) · doi:10.1103/PhysRevD.13.3398
[10] Chodos, A., et al.: Phys. Rev. D 9, 3471 (1974) · doi:10.1103/PhysRevD.9.3471
[11] Ho, C.L.: Ann. Phys. 321, 2170 (2006) · Zbl 1097.81027 · doi:10.1016/j.aop.2005.12.005
[12] Bender, C.M., Boettcher, S.: Phys. Rev. Lett. 80, 5243 (1998) · Zbl 0947.81018 · doi:10.1103/PhysRevLett.80.5243
[13] Bender, C.M., Boettcher, S., Meisinger, P.N.: J. Math. Phys. 40, 2201 (1999) · Zbl 1057.81512 · doi:10.1063/1.532860
[14] Bagchi, B., Cannata, F., Quesne, C.: Phys. Lett. A 269, 79 (2000) · Zbl 1115.81392 · doi:10.1016/S0375-9601(00)00227-9
[15] Khare, A., Mandal, B.P.: Phys. Lett. A 272, 53 (2000) · Zbl 1115.81395 · doi:10.1016/S0375-9601(00)00409-6
[16] Buslaev, V., Grecchi, V.: J. Phys. A: Math. Gen. 26, 5541 (1993) · Zbl 0817.47077 · doi:10.1088/0305-4470/26/20/035
[17] Znojil, M., Lévai, G.: Phys. Lett. A 271, 327 (2000) · Zbl 1115.81339 · doi:10.1016/S0375-9601(00)00400-X
[18] Bagchi, B., Mallik, S., Quesne, C., Roychoudhury, R.: Phys. Lett. A 289, 34 (2001) · Zbl 0972.81026 · doi:10.1016/S0375-9601(01)00578-3
[19] Dorey, P., Dunning, C., Tateo, R.: J. Phys. A: Math. Gen. 4, 5679 (2001) · Zbl 0982.81021 · doi:10.1088/0305-4470/34/28/305
[20] Kretschmer, R., Szymanowski, L.: Czechoslov. J. Phys. 54, 71 (2004) · doi:10.1023/B:CJOP.0000014370.87951.43
[21] Znojil, M., Gemperle, F., Mustafa, O.: J. Phys. A: Math. Gen. 35, 5781 (2002) · Zbl 1066.81006 · doi:10.1088/0305-4470/35/27/317
[22] Mustafa, O., Znojil, M.: J. Phys. A: Math. Gen. 35, 8929 (2002) · Zbl 1042.81019 · doi:10.1088/0305-4470/35/42/304
[23] Ahmed, Z.: Phys. Lett. A 290, 19 (2001) · Zbl 1020.81016 · doi:10.1016/S0375-9601(01)00622-3
[24] Mostafazadeh, A.: J. Math. Phys. 43, 2814 (2002) · Zbl 1060.81022 · doi:10.1063/1.1461427
[25] Mostafazadeh, A.: Nucl. Phys. B 640, 419 (2002) · Zbl 0997.81031 · doi:10.1016/S0550-3213(02)00347-4
[26] Mostafazadeh, A.: J. Math. Phys. 44, 974 (2003) · Zbl 1061.81076 · doi:10.1063/1.1539304
[27] Mostafazadeh, A.: J. Phys. A: Math. Gen. 38, 3213 (2005) · Zbl 1088.81044 · doi:10.1088/0305-4470/38/14/011
[28] Sinha, A., Roy, P.: Czechoslov. J. Phys. 54, 129 (2004) · doi:10.1023/B:CJOP.0000014377.24971.31
[29] Jiang, L., Yi, L.Z., Jia, C.S.: Phys. Lett. A 345, 279 (2005) · Zbl 1345.81036 · doi:10.1016/j.physleta.2005.07.045
[30] Mandal, B.P.: Mod. Phys. Lett. A 20, 655 (2005) · Zbl 1067.81535 · doi:10.1142/S0217732305016488
[31] Znojil, M., Bíla, H., Jakubsky, V.: Czechoslov. J. Phys. 54, 1143 (2004) · doi:10.1023/B:CJOP.0000044017.33267.58
[32] Mostafazadeh, A., Batal, A.: J. Phys. A: Math. Gen. 37, 11645 (2004) · Zbl 1064.81057 · doi:10.1088/0305-4470/37/48/009
[33] Mustafa, O.: J. Phys. A: Math. Gen. 36, 5067 (2003) · Zbl 1028.81013 · doi:10.1088/0305-4470/36/18/311
[34] Bagchi, B., Quesne, C.: Phys. Lett. A 301, 173 (2002) · Zbl 0997.81027 · doi:10.1016/S0375-9601(02)00929-5
[35] Znojil, M.: Phys. Lett. A 259, 220 (1999) · Zbl 0948.81535 · doi:10.1016/S0375-9601(99)00429-6
[36] Solombrino, L.: J. Math. Phys. 43, 5439 (2002) · Zbl 1060.81026 · doi:10.1063/1.1504485
[37] Mustafa, O., Mazharimousavi, S.H.: Czechoslov. J. Phys. 56, 967 (2006) · Zbl 1110.81087 · doi:10.1007/s10582-006-0392-z
[38] Mustafa, O., Mazharimousavi, S.H.: Phys. Lett. A 357, 295 (2006) · Zbl 05358644 · doi:10.1016/j.physleta.2006.06.027
[39] Jia, C.S., de Souza Dutra, A.: J. Phys. A: Math. Gen. 39, 11877 (2006) · Zbl 1100.81018 · doi:10.1088/0305-4470/39/38/013
[40] Mustafa, O., Mazharimousavi, S.H.: J. Phys. A: Math. Theor. 40, 863 (2007) · Zbl 1108.81023 · doi:10.1088/1751-8113/40/4/N01
[41] Quesne, C.: Ann. Phys. 321, 1221 (2006) · Zbl 1092.81016 · doi:10.1016/j.aop.2005.11.013
[42] Quesne, C., Tkachuk, V.M.: J. Phys. A: Math. Gen. 37, 4267 (2004) · Zbl 1063.81070 · doi:10.1088/0305-4470/37/14/006
[43] Tanaka, T.: J. Phys. A: Math. Gen. 39, 219 (2006) · Zbl 1092.81031 · doi:10.1088/0305-4470/39/1/016
[44] von Roos, O.: Phys. Rev. B 27, 7547 (1983) · doi:10.1103/PhysRevB.27.7547
[45] Gang, C.: Phys. Lett. A 329, 22 (2004) · Zbl 1160.81370 · doi:10.1016/j.physleta.2004.06.086
[46] Jiang, L., Yi, L.Z., Jia, C.S.: Phys. Lett. A 345, 279 (2005) · Zbl 1345.81036 · doi:10.1016/j.physleta.2005.07.045
[47] Mustafa, O., Mazharimousavi, S.H.: Phys. Lett. A 358, 259 (2006) · Zbl 1142.81327 · doi:10.1016/j.physleta.2006.05.037
[48] Mustafa, O., Mazharimousavi, S.H.: J. Phys. A: Math. Gen. 39, 10537 (2006) · Zbl 1114.81031 · doi:10.1088/0305-4470/39/33/020
[49] Alhaidari, A.D.: Int. J. Theor. Phys. 42, 2999 (2003) · Zbl 1040.81008 · doi:10.1023/B:IJTP.0000006027.49538.16
[50] Alhaidari, A.D.: Phys. Rev. A 66, 042116 (2002) · Zbl 1016.81021 · doi:10.1103/PhysRevA.66.042116
[51] Puente, A., Casas, M.: Comput. Mater Sci. 2, 441 (1994) · doi:10.1016/0927-0256(94)90070-1
[52] Bastard, G.: Wave Mechanics Applied to Semiconductor Heterostructures. Les Editions de Physique, Les Ulis (1988)
[53] Serra, L.I., Lipparini, E.: Europhys. Lett. 40, 667 (1997) · doi:10.1209/epl/i1997-00520-y
[54] Bagchi, B., Quesne, C.: Phys. Lett. A 300, 173 (2002) · Zbl 0997.81027 · doi:10.1016/S0375-9601(02)00929-5
[55] Samsonov, B.F., Roy, P.: J. Phys. A: Math. Gen. 38, L249 (2005) · Zbl 1065.81048 · doi:10.1088/0305-4470/38/15/L02
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.