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Periodic Hamiltonian hierarchies and non-uniqueness of superpotentials

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Abstract

In this article, a family of periodic quantum Hamiltonians, that is subject to a closure condition is considered. In the context of the factorization method, we address the question of non-uniqueness of the governing superpotentials and study an alternative factorization to generate new hierarchies of potentials.

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References

  1. L E Gendenshtein and I V Ikrine, Sov. Phys. Usp. 28, 645 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  2. G Junker, Supersymmetric methods in quantum and statistical physics (Springer, Berlin, 1996)

    Book  MATH  Google Scholar 

  3. B K Bagchi, Supersymmetry in quantum and classical mechanics (Chapman and Hall, London, 2001)

    MATH  Google Scholar 

  4. F Cooper, A Khare, and U Sukhatme, Supersymmetry in quantum mechanics (World Scientific, Singapore, 2001)

    Book  MATH  Google Scholar 

  5. D J Fernandez, AIP Conf. Proc 1287, 3 (2010)

    ADS  Google Scholar 

  6. A A Andrianov and M V Ioffe, J. Phys. A 45, 503001 (2012)

    Article  Google Scholar 

  7. L Infeld and T E Hull, Rev. Mod. Phys. 23, 21 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  8. B Mielnik and O Rosas-Ortiz, J. Phys. A: Math. Gen. 37, 10007 (2004)

    Article  ADS  Google Scholar 

  9. A B Shabat and R I Yamilov, Leningrad Math. J. 2, 577 (1991)

    Google Scholar 

  10. V Spiridonov, Commun. Theor. Phys. 2, 149 arXiv:hep-th/9303004 (1993)

  11. V E Adler, Physica D 73, 335 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  12. U P Sukhatme, C Rasinariu, and A Khare, Phys. Lett. A 234, 401 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  13. D Bermudez and D J Fernndez arXiv:1311.0647(2013)

  14. D J Iyela, J Govaerts, and M N Hounkonnou, J. Math. Phys. 54, 093502 arXiv:1209.0182

  15. B Mielnik, J. Math. Phys. 25, 3387 (1984)

    Article  ADS  Google Scholar 

  16. C N Kumar, J. Phys. A: Math. Gen. 20, 5397 (1987)

    Article  ADS  Google Scholar 

  17. P Cherian, K Abhinav, and P K Panigrahi arXiv:1110.3708 (2013)

  18. A Das and S A Pernice, Nucl. Phys. B 561, 357 (1999)

    Article  ADS  Google Scholar 

  19. V De Alfaro, S Fubini, and G Furlan, Nuovo Cimento A 34, 569 (1976)

    Article  ADS  Google Scholar 

  20. A P Veselov and A B Shabat, Funct. Anal. Appl. 27, 81 (1993)

    Article  MathSciNet  Google Scholar 

  21. M S Berger and N S Ussembayev, Phys. Rev. A 82, 022121 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  22. A Mitra, P K Roy, A Lahiri, and B Bagchi, Int. J. Theor. Phys. 28, 911 (1989)

    Article  Google Scholar 

  23. Y Grandati arXiv:1108.4503 (2011)

Download references

Acknowledgements

The authors thank Prof. B Bagchi, Department of Applied Mathematics, University of Calcutta for his valuable advice. PM thanks the Council of Scientific and Industrial Research, New Delhi for the award of senior research fellowship. The authors also thank the referee for making a number of constructive suggestions that have helped in the improvement of the paper.

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Correspondence to Abhijit Banerjee.

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Mandal, P., Banerjee, A. Periodic Hamiltonian hierarchies and non-uniqueness of superpotentials. Pramana - J Phys 88, 1 (2017). https://doi.org/10.1007/s12043-016-1302-y

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  • DOI: https://doi.org/10.1007/s12043-016-1302-y

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