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(1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively \(\mathcal{PT}\) -Symmetric

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Abstract

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 η-weak-pseudo-Hermiticity generator are presented and a complexified \(\mathcal{PT}\) -symmetric periodic-type model is used as an illustrative example.

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References

  1. Nogami, N., Toyama, F.M.: Phys. Rev. A 47, 1708 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  2. Nogami, N., Toyama, F.M.: Phys. Rev. A 57, 93 (1998)

    Article  ADS  Google Scholar 

  3. Witten, E.: Nucl. Phys. B 188, 513 (1981)

    Article  ADS  Google Scholar 

  4. Cooper, F., Khare, A., Sukhatme, U.: Phys. Rep. 251, 267 (1995)

    Article  MathSciNet  Google Scholar 

  5. Sukumar, C.V.: J. Phys. A: Math. Gen. 18, 2917 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  6. Cooper, F., et al.: Ann. Phys. 187, 1 (1987)

    ADS  Google Scholar 

  7. de Castro, A.S., Hott, M.: Phys. Lett. A 342, 53 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  8. Sinha, A., Roy, P.: Mod. Phys. Lett. A 20, 2377 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. Jackiw, R., Rebbi, C.: Phys. Rev. D 13, 3398 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  10. Chodos, A., et al.: Phys. Rev. D 9, 3471 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  11. Ho, C.L.: Ann. Phys. 321, 2170 (2006)

    Article  MATH  ADS  Google Scholar 

  12. Bender, C.M., Boettcher, S.: Phys. Rev. Lett. 80, 5243 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Bender, C.M., Boettcher, S., Meisinger, P.N.: J. Math. Phys. 40, 2201 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. Bagchi, B., Cannata, F., Quesne, C.: Phys. Lett. A 269, 79 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Khare, A., Mandal, B.P.: Phys. Lett. A 272, 53 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Buslaev, V., Grecchi, V.: J. Phys. A: Math. Gen. 26, 5541 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. Znojil, M., Lévai, G.: Phys. Lett. A 271, 327 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  18. Bagchi, B., Mallik, S., Quesne, C., Roychoudhury, R.: Phys. Lett. A 289, 34 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. Dorey, P., Dunning, C., Tateo, R.: J. Phys. A: Math. Gen. 4, 5679 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  20. Kretschmer, R., Szymanowski, L.: Czechoslov. J. Phys. 54, 71 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  21. Znojil, M., Gemperle, F., Mustafa, O.: J. Phys. A: Math. Gen. 35, 5781 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. Mustafa, O., Znojil, M.: J. Phys. A: Math. Gen. 35, 8929 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. Ahmed, Z.: Phys. Lett. A 290, 19 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. Mostafazadeh, A.: J. Math. Phys. 43, 2814 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. Mostafazadeh, A.: Nucl. Phys. B 640, 419 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. Mostafazadeh, A.: J. Math. Phys. 44, 974 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. Mostafazadeh, A.: J. Phys. A: Math. Gen. 38, 3213 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  28. Sinha, A., Roy, P.: Czechoslov. J. Phys. 54, 129 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  29. Jiang, L., Yi, L.Z., Jia, C.S.: Phys. Lett. A 345, 279 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  30. Mandal, B.P.: Mod. Phys. Lett. A 20, 655 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  31. Znojil, M., Bíla, H., Jakubsky, V.: Czechoslov. J. Phys. 54, 1143 (2004)

    Article  ADS  Google Scholar 

  32. Mostafazadeh, A., Batal, A.: J. Phys. A: Math. Gen. 37, 11645 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. Mustafa, O.: J. Phys. A: Math. Gen. 36, 5067 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  34. Bagchi, B., Quesne, C.: Phys. Lett. A 301, 173 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  35. Znojil, M.: Phys. Lett. A 259, 220 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. Solombrino, L.: J. Math. Phys. 43, 5439 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  37. Mustafa, O., Mazharimousavi, S.H.: Czechoslov. J. Phys. 56, 967 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  38. Mustafa, O., Mazharimousavi, S.H.: Phys. Lett. A 357, 295 (2006)

    Article  ADS  Google Scholar 

  39. Jia, C.S., de Souza Dutra, A.: J. Phys. A: Math. Gen. 39, 11877 (2006)

    Article  MATH  ADS  Google Scholar 

  40. Mustafa, O., Mazharimousavi, S.H.: J. Phys. A: Math. Theor. 40, 863 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  41. Quesne, C.: Ann. Phys. 321, 1221 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  42. Quesne, C., Tkachuk, V.M.: J. Phys. A: Math. Gen. 37, 4267 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  43. Tanaka, T.: J. Phys. A: Math. Gen. 39, 219 (2006)

    Article  MATH  ADS  Google Scholar 

  44. von Roos, O.: Phys. Rev. B 27, 7547 (1983)

    Article  ADS  Google Scholar 

  45. Gang, C.: Phys. Lett. A 329, 22 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  46. Jiang, L., Yi, L.Z., Jia, C.S.: Phys. Lett. A 345, 279 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  47. Mustafa, O., Mazharimousavi, S.H.: Phys. Lett. A 358, 259 (2006)

    Article  ADS  Google Scholar 

  48. Mustafa, O., Mazharimousavi, S.H.: J. Phys. A: Math. Gen. 39, 10537 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  49. Alhaidari, A.D.: Int. J. Theor. Phys. 42, 2999 (2003)

    Article  MATH  Google Scholar 

  50. Alhaidari, A.D.: Phys. Rev. A 66, 042116 (2002)

    Article  ADS  Google Scholar 

  51. Puente, A., Casas, M.: Comput. Mater Sci. 2, 441 (1994)

    Article  Google Scholar 

  52. Bastard, G.: Wave Mechanics Applied to Semiconductor Heterostructures. Les Editions de Physique, Les Ulis (1988)

    Google Scholar 

  53. Serra, L.I., Lipparini, E.: Europhys. Lett. 40, 667 (1997)

    Article  ADS  Google Scholar 

  54. Bagchi, B., Quesne, C.: Phys. Lett. A 300, 173 (2002)

    Article  ADS  Google Scholar 

  55. Samsonov, B.F., Roy, P.: J. Phys. A: Math. Gen. 38, L249 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics, Eastern Mediterranean University, G Magusa, North Cyprus, Mersin 10, Turkey

    Omar Mustafa & S. Habib Mazharimousavi

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  1. Omar Mustafa
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  2. S. Habib Mazharimousavi
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Correspondence to Omar Mustafa.

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Mustafa, O., Mazharimousavi, S.H. (1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively \(\mathcal{PT}\) -Symmetric. Int J Theor Phys 47, 1112–1120 (2008). https://doi.org/10.1007/s10773-007-9539-3

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  • DOI: https://doi.org/10.1007/s10773-007-9539-3

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