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Sturm-Schrödinger equations: Formula for metric

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Abstract

Sturm-Schrödinger equations Hψ = EWψ with H ≠ H † and W≠ = W † ≠ = I are considered, with a weak point of the theory lying in the purely numerical matrix-inversion form of the double-series definition of the necessary metric operator Θ in the physical Hilbert space of states [M Znojil, J. Phys. A: Math. Theor. 41, 215304 (2008]. This shortcoming is removed here via an amended, single-series definition of Θ.

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References

  1. L Liouville, J. Math. Pure Appl. 1, 16 (1837)

    Google Scholar 

  2. M Znojil, J. Phys. A: Math. Gen. 27, 4945 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. M Znojil, J. Phys. A: Math. Theor. 41, 215304 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  4. G J C Wessels, A numerical and analytical investigation into non-Hermitian Hamiltonians, Master-degree thesis supervised by H B Geyer and J A C Weideman (University of Stellenbosch, 2008)

  5. F G Scholtz, H B Geyer and F J W Hahne, Ann. Phys. (N.Y.) 213, 74 (1992)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. M Znojil, SIGMA 4, 001 (2008), arXiv overlay: 0710.4432v3 [math-ph]

    MathSciNet  Google Scholar 

  7. A Messiah, Quantum mechanics I (North Holland, Amsterdam, 1961)

    Google Scholar 

  8. M Znojil, Phys. Lett. A372, 584, 3591 (2008)

    MathSciNet  ADS  Google Scholar 

  9. M Znojil, J. Phys. Conf. Ser. 128, 012046 (2008)

    Article  ADS  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. A Mostafazadeh, J. Phys. A: Math. Gen. 38, 6557 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. M Rotenberg, Adv. At. Mol. Phys. 6, 233 (1970)

    Article  Google Scholar 

  13. M Znojil, J. Math. Phys. 38, 5087 (1997)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. A Voros, J. Phys. A: Math. Gen. 33, 7423 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. R Szmytkowski and B Zywicka-Mozejko, Phys. Rev. A62, 022104 (2000)

    MathSciNet  ADS  Google Scholar 

  16. C M Bender and Q Wang, J. Phys. A: Math. Gen. 34, 9835 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. E Kelbert, A Hyder, F Demir, Z T Hlousek and Z Papp, J. Phys. A: Math. Theor. 40, 7721 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Nuclear Physics Institute ASCR, 250 68, Řež, Czech Republic

    Miloslav Znojil

  2. Institute of Theoretical Physics, University of Stellenbosch and Stellenbosch Institute for Advanced Study, 7600, Stellenbosch, South Africa

    Hendrik B. Geyer

Authors
  1. Miloslav Znojil
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  2. Hendrik B. Geyer
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Correspondence to Miloslav Znojil.

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Znojil, M., Geyer, H.B. Sturm-Schrödinger equations: Formula for metric. Pramana - J Phys 73, 299–306 (2009). https://doi.org/10.1007/s12043-009-0121-9

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