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Factorization of nonlinear supersymmetry in one-dimensional quantum mechanics. III: precise classification of irreducible intertwining operators

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In this part of the work, we present a detailed classification of first order intertwining operators and of really irreducible intertwining second order operators of I, II, and III types. This classification is constructed in dependence of kernel structures of these operators and relations between spectra of intertwined Hamiltonians. It was shown earlier that one can construct from such operators any intertwining operator of arbitrary order with the help of chain (ladder) construction. Bibliography: 25 titles.

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References

  1. A. A. Andrianov and A. V. Sokolov, Zap. Nauchn. Semin. POMI, 335, 22 (2006); arXiv: 0710.5738 [quant—ph].

    MATH  Google Scholar 

  2. A. V. Sokolov, Zap. Nauchn. Semin. POMI 347, 214 (2007); arXiv: 0903.2835 [math—ph].

    Google Scholar 

  3. E. Schrödinger, Proc. Roy. Irish Acad. A, 47, 53 (1941) [physics/9910003].

    MATH  Google Scholar 

  4. L. Infeld and T. E. Hull, Rev. Mad. Phys., 23, 21 (1951).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. A. Andrianov. N. V. Borisov, M. V. Ioffe, and M. I. Eides, Teor. Mat. Fiz., 61, 965 (1984); Phys. Lett. A. 109, 143 (1985).

    Google Scholar 

  6. C. V. Sukumar, J. Phys. A: Math. Gen., 18, L57, 2917 (1985).

    Article  MathSciNet  Google Scholar 

  7. A. A. Andrianov and F. Cannata, J. Phys. A, Math. Gen., 37, 10297 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Cooper and B. Freedman, Ann. Phys., 146, 262 (1983).

    Article  MathSciNet  Google Scholar 

  9. L. Trlifaj, Inv. Prob., 5, 1145 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  10. D. J. Fernández, B. Mielnik, O. Rosas-Ortiz. and B. F. Samsonov, J. Phys. A. 35, 4279 (2002); quant-ph/0303051.

    Article  MATH  MathSciNet  Google Scholar 

  11. D. J. Fernández, B. Mielnik, O. Rosas-Ortiz. and B. F. Samsonov, Phys. Lett. A, 294, 168 (2002); quant—ph/0302204.

    Article  MATH  MathSciNet  Google Scholar 

  12. G. Dunne and J. Feinberg, Phys. Rev. D, 57, 1271 (1998); hep-th/9706012.

    Article  MathSciNet  Google Scholar 

  13. A. Khare and U. Sukhatme, J. Math;. Phys., 40, 5473 (1999); quant-ph/9906044.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. A. Andrianov, F. Cannata, J.—P. Dedonder, and M. V. Ioffe, Int. J. Mod. Phys. A, 10, 2683 (1995); hep—th/9404061.

    Article  MATH  MathSciNet  Google Scholar 

  15. D. J. Fernández, R. Muñoz, and A. Ramos, Phys. Lett. A, 308, 11 (2003); quant-ph/02].2026.

    Article  MATH  MathSciNet  Google Scholar 

  16. D. J. Fernández, J. Negro, and L. M. Nieto, Phys. Lett. A, 275, 338 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  17. B. F. Samsonov, Phys. Lett. A, 263, 274 (1999); quant-ph/9904009.

    Article  MATH  MathSciNet  Google Scholar 

  18. D. J. Fernández and E. Salinas-Hernández, J. Phys. A, 36, 2537 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  19. G. Darboux, C. R. Acad. Sci. (Paris), 94, 1456 (1882) [physics/9908003].

    Google Scholar 

  20. M. M. Crum, Quart. J. Math. (Oxford), 6, 121 (1955) [physics/9908019].

    Article  MATH  MathSciNet  Google Scholar 

  21. A. A. Andrianov, M. V. Ioffe, and V. P. Spirinov, Phys. Lett. A, 174, 273 (1993); preprint hep-th/9303005.

    Article  MathSciNet  Google Scholar 

  22. A. A. Andrianov and A. Y. Sokolov, Nucl. Physl B, 660, 25 (2003); hep-th/0301062.

    Article  MATH  MathSciNet  Google Scholar 

  23. M. A. Naimark, Linear Differential Operators, Frederick Ungar Publishing Co., New York (1967).

    MATH  Google Scholar 

  24. V. G. Bagrov and B. F. Samsonov, Phys. Part. Nucl., 28, 374 (1997).

    Article  MathSciNet  Google Scholar 

  25. A. V. Sokolov, Nucl. Phys. B, 773, 137 (2007); math—ph/0610022.

    Article  MATH  Google Scholar 

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  1. St.Petersburg State University, St.Petersburg, Russia

    A. V. Sokolov

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  1. A. V. Sokolov
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Correspondence to A. V. Sokolov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 374, 2010, pp. 213–2494, 2010.

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Sokolov, A.V. Factorization of nonlinear supersymmetry in one-dimensional quantum mechanics. III: precise classification of irreducible intertwining operators. J Math Sci 168, 881–900 (2010). https://doi.org/10.1007/s10958-010-0035-6

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  • DOI: https://doi.org/10.1007/s10958-010-0035-6

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