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Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators

  • Elementary Particles and Fields
  • Theory
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Abstract

The metric operator, which is the basic ingredient for studying a quantum system described by a pseudo-Hermitian Hamiltonian, provides the necessary means for obtaining an equivalent description of the system using a Hermitian Hamiltonian. In the framework of supersymmetric quantum mechanics, we propose a method of constructing the metric operator and to obtain the Hermitian Hamiltonian equivalent to the given pseudo-Hermitian.

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References

  1. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 89, 270401 (2002).

    Article  MathSciNet  Google Scholar 

  2. C. M. Bender, D. C. Brody, and H. F. Jones, Am. J. Phys. 71, 1095 (2003).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. V. Jakubský, Acta Polytech. 47, 71 (2007).

    Google Scholar 

  4. A. Mostafazadeh, J. Math. Phys. 43, 205 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. A. Mostafazadeh, J. Math. Phys. 43, 3944 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. A. Mostafazadeh, Class. Quantum Grav. 20, 155 (2003).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. C.M. Bender, P. N. Meisinger, and Q. Wang, J. Phys. A 36, 1973 (2003).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. C. M. Bender, J. Brod, A. Refig, and M. E. Reuter, J. Phys. A 37, 10139 (2004).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 93, 251601 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  11. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 70, 025001 (2004).

    Article  ADS  Google Scholar 

  12. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 71, 049901 (Erratum) (2005).

    ADS  Google Scholar 

  13. A. Mostafazadeh and A. Batal, J. Phys. A 37, 11645 (2004).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. A. Mostafazadeh, J. Phys. A 38, 6557 (2005).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. C. M. Bender, I. Cavero-Pelaez, K. A. Milton, and K. V. Shajesh, Phys. Lett. B 613, 97 (2005).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. T. V. Fityo, J. Phys. A 35, 5893 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. O. Mustafa and S. H. Mazharimousavi, Phys. Lett. A 357, 295 (2006).

    Article  ADS  Google Scholar 

  18. U. Gunther and B. F. Samsonov, Phys. Rev. A 78, 042115 (2008).

    Article  MathSciNet  ADS  Google Scholar 

  19. A. Mostafazadeh, J. Math. Phys. 43, 6343 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  20. B.F. Samsonov, V. V. Shamshutdinova, and A. V. Osipov, Phys. Lett. A 374, 1962 (2010).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. B. F. Samsonov, J. Phys. A 43, 402006 (2010).

    Article  MathSciNet  Google Scholar 

  22. B. M. Levitan and I. S. Sargsyan, Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators, Translations of Mathematical Monographs (Providence, Rhode Island, 1975).

  23. A. A. Andrianov, F. Cannata, J.-P. Dedonder, and M. V. Ioffe, Int. J. Mod. Phys. A 14, 2675 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 246, 219 (1998).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. F. Cannata, M. V. Ioffe, R. Roychoudhury, and P. Roy, Phys. Lett. A 281, 305 (2001).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. A. A. Andrianov, F. Cannata, and A. V. Sokolov, Nucl. Phys. B 773, 107 (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. A. V. Sokolov, Nucl. Phys. B 773, 137 (2007).

    Article  ADS  MATH  Google Scholar 

  28. B. F. Samsonov, J. Phys. A 38, L397 (2005).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. B. F. Samsonov and P. Roy, J. Phys. A 38, L249 (2005).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. D. Krejčiřík, H. Bíla, and M. Znojil, J. Phys. A 39, 10143 (2006).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. D. Krejčiřík, J. Phys. A 41, 244012 (2008).

    Article  MathSciNet  ADS  Google Scholar 

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Correspondence to V. V. Shamshutdinova.

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Shamshutdinova, V.V. Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators. Phys. Atom. Nuclei 75, 1294–1298 (2012). https://doi.org/10.1134/S1063778812100183

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  • DOI: https://doi.org/10.1134/S1063778812100183

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