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Darboux Transformation of the Nonstationary Dirac Equation

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Abstract

The method of differential transformation operators is applied to the Dirac equation with the generalized form of the time-dependent potential. It is demonstrated that the transformation operator and the transformed potential are solutions of the initial equation. It is established that under certain conditions, an integral expression can be retrieved for the transformed potential. Examples of new potentials expressed through elementary functions are presented for which the Dirac equation can be solved exactly.

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REFERENCES

  1. V. F. Bagrov and B. F. Samsonov, Fiz. Elem. Chast. Atomn. Yadra, 28, 951 (1997).

    Google Scholar 

  2. V. Matveev and M. Salle, Darboux Transformations and Solutions, Springer, New-York (1991).

    Google Scholar 

  3. V. G. Bagrov and B. F. Samsonov, Teor. Matem. Fiz., 104, 356–367 (1995).

    Google Scholar 

  4. A. Anderson, Phys. Rev., A43, 4602 (1991).

    Google Scholar 

  5. A. A. Stahlhofen, J. Phys., A27, 8279 (1994).

    Google Scholar 

  6. A. V. Yurov, Phys. Lett., A225, 51 (1997).

    Google Scholar 

  7. B. F. Samsonov and A. A. Pecheritsyn, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 48 (2000).

  8. L. M. Nieto, A. A. Pecheritsyn, and B. F. Samsonov, Ann. Phys., 305, 151 (2003).

    Article  Google Scholar 

  9. B. Thaler, The Dirac Equation, Springer, Berlin (1992).

    Google Scholar 

  10. G. Soff, B. Muller, J. Rafelski, and W. Greiner, Z. Naturforsch., A26, 1389 (1973).

    Google Scholar 

  11. F. Dominguez-Adame, Am. J. Phys., 58, 886 (1990).

    Article  Google Scholar 

  12. B. M. Levitan and I. S. Sargsyan, Introduction to Spectral Theory [in Russian], Moscow, Nauka (1970).

    Google Scholar 

  13. B. F. Samsonov and J. Negro, J. Phys., A37, 10115 (2004).

    Google Scholar 

  14. B. F. Samsonov and A. A. Pecheritsyn, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 1, 74 (2002).

  15. B. F. Samsonov, J. Phys., A28, 6989 (1995).

    Google Scholar 

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Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    A. A. Pecheritsyn, E. O. Pozdeeva & B. F. Samsonov

Authors
  1. A. A. Pecheritsyn
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  2. E. O. Pozdeeva
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  3. B. F. Samsonov
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__________

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–41, April, 2005.

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Pecheritsyn, A.A., Pozdeeva, E.O. & Samsonov, B.F. Darboux Transformation of the Nonstationary Dirac Equation. Russ Phys J 48, 365–374 (2005). https://doi.org/10.1007/s11182-005-0134-x

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  • DOI: https://doi.org/10.1007/s11182-005-0134-x

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