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Scattering theory for one-dimensional systems with nontrivial spatial asymptotics

Part of the Lecture Notes in Mathematics book series (LNM,volume 1218)

Keywords

  • Total Reflection
  • Case Versus
  • Topological Invariance
  • Energy Regime
  • Fredholm Determinant

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References

  1. R. Akhoury and A. Comtet, Nucl. Phys. B246 (1984), 253–278.

    CrossRef  ADS  MathSciNet  Google Scholar 

  2. N.A. Alves, H. Aratyn and A.H. Zimmerman, Phys. Rev. D31 (1985), 3298–3300.

    ADS  Google Scholar 

  3. H. Baumgärtel and M. Wollenberg, "Mathematical Scattering Theory", Birkhäuser, Basel, 1983.

    CrossRef  MATH  Google Scholar 

  4. M.S. Birman and M.G. Krein, Sov. Math. Dokl. 3 (1962), 740–744.

    Google Scholar 

  5. D.Bollé, F.Gesztesy, H.Grosse and W.Schweiger, paper in preparation.

    Google Scholar 

  6. P.J.M. Bongaarts and S.N.M. Ruijsenaars, Ann. Inst. H.Poincaré A26 (1977), 1–17.

    MathSciNet  Google Scholar 

  7. D. Boyanovsky and R. Blankenbecler, Phys. Rev. D30 (1984), 1821–1824.

    ADS  MathSciNet  Google Scholar 

  8. D. Boyanovsky and R. Blankenbecler, Phys. Rev. D31 (1985), 3234–3250.

    ADS  MathSciNet  Google Scholar 

  9. H. Bremermann, "Distributions, Complex Variables and Fourier Transforms", Addison-Wesley, New York, 1965.

    MATH  Google Scholar 

  10. V.S. Buslaev, "Theoret. Math. Phys. 58 (1984), 153–159.

    CrossRef  MathSciNet  Google Scholar 

  11. V.S. Buslaev and L.D. Faddeev, Sov. Math. Dokl. 1 (1960), 451–454.

    MathSciNet  Google Scholar 

  12. E. Caliceti, Ann. Inst. H.Poincaré A42 (1985), 235–251.

    MathSciNet  Google Scholar 

  13. C. Callias, Commun. Math. Phys. 62 (1978), 213–234.

    CrossRef  ADS  MathSciNet  Google Scholar 

  14. K. Chadan and P.C. Sabatier, "Inverse Problems in Quantum Scattering Theory", Springer, New York, 1977.

    CrossRef  MATH  Google Scholar 

  15. A. Cohen and T. Kappeler, Indiana Univ. Math. J. 34 (1985), 127–180.

    CrossRef  MathSciNet  Google Scholar 

  16. E.B. Davies and B. Simon, Commun. Math. Phys. 63 (1978), 277–301.

    CrossRef  ADS  MathSciNet  Google Scholar 

  17. P.A. Deift, Duke Math. J. 45 (1978), 267–310.

    CrossRef  MathSciNet  Google Scholar 

  18. P. Deift and E. Trubowitz, Commun. Pure Appl. Math. 32 (1979), 121–251.

    CrossRef  MathSciNet  Google Scholar 

  19. N.E. Firsova, J. Sov. Math. 11 (1979), 487–497.

    CrossRef  Google Scholar 

  20. N.E. Firsova, Theoret. Math. Phys. 62 (1985), 130–140.

    CrossRef  MathSciNet  Google Scholar 

  21. F. Gesztesy, W. Plessas and B. Thaller, J. Phys. A13 (1980), 2659–2671.

    ADS  MathSciNet  Google Scholar 

  22. F.Gesztesy and B.Simon, paper in preparation.

    Google Scholar 

  23. I.C. Gohberg and M.G. Krein, "Introduction to the Theory of Linear Nonselfadjoint Operators", AMS, Providence, 1969.

    MATH  Google Scholar 

  24. I.S. Gradshteyn and I.M. Ryzhik, "Table of Integrals, Series, and Products", Academic, New York, 1965.

    MATH  Google Scholar 

  25. M. Hirayama, Progr. Theoret. Phys. 70 (1983), 1444–1453.

    CrossRef  ADS  MathSciNet  Google Scholar 

  26. M. Hirayama, Phys. Lett. 156B (1985), 225–230.

    CrossRef  ADS  MathSciNet  Google Scholar 

  27. C. Imbimbo and S. Mukhi, Nucl. Phys. B242 (1984), 81–92.

    CrossRef  ADS  MathSciNet  Google Scholar 

  28. T.D. Imbo and U.P. Sukhatme, Phys. Rev. Lett. 54 (1985), 2184–2187.

    CrossRef  ADS  Google Scholar 

  29. A. Jensen and T. Kato, Commun. Part. Diff. Eqs. 3 (1978), 1165–1195.

    CrossRef  MathSciNet  Google Scholar 

  30. T. Kato, "Perturbation Theory for Linear Operators", Springer, Berlin, 1980.

    MATH  Google Scholar 

  31. W. Kohn, Phys. Rev. 115 (1959), 809–821.

    CrossRef  ADS  MathSciNet  Google Scholar 

  32. V.A. Kostelecky and M.M. Nieto, Phys. Rev. A32 (1985), 1293–1298.

    CrossRef  ADS  MathSciNet  Google Scholar 

  33. M.G. Krein, Sov. Math. Dokl. 3 (1962), 707–710.

    Google Scholar 

  34. M.G. Krein, "Topics in Differential and Integral Equations and Operator Theory", I. Gohberg (ed.), Birkhäuser, Basel, 1983, p. 107.

    CrossRef  Google Scholar 

  35. J. Lott, Commun. Math. Phys. 93 (1984), 533–558.

    CrossRef  ADS  MathSciNet  Google Scholar 

  36. R.G. Newton, J.Math. Phys. 21 (1980), 493–505.

    CrossRef  ADS  MathSciNet  Google Scholar 

  37. R.G. Newton, "Scattering Theory of Waves and Particles", Springer, New York, 1982.

    CrossRef  MATH  Google Scholar 

  38. R.G. Newton, J. Math. Phys. 24 (1983), 2152–2162; 26 (1985), 311–316.

    CrossRef  ADS  MathSciNet  Google Scholar 

  39. A.J.Niemi and G.W.Semenoff, "Fermion Number Fractionization in Quantum Field Theory" to appear in Phys. Rep. (1986).

    Google Scholar 

  40. A.J. Niemi and L.C.R. Wijewardhana, Phys. Lett. 138B (1984), 389–392.

    CrossRef  ADS  MathSciNet  Google Scholar 

  41. D.B. Pearson, Helv. Phys. Acta 47 (1974), 249–264.

    MathSciNet  Google Scholar 

  42. M. Reed and B. Simon, "Methods of Modern Mathematical Physics III. Scattering Theory", Academic, New York, 1979.

    MATH  Google Scholar 

  43. M. Reed and B. Simon, "Methods of Modern Mathematical Physics IV. Analysis of Operators", Academic, New York, 1978.

    MATH  Google Scholar 

  44. U.W. Schmincke, Proc. Roy. Soc. Edinburgh 80A (1978), 67–84.

    CrossRef  MathSciNet  Google Scholar 

  45. B. Simon, "Trace Ideals and their Applications", Cambridge Univ. Press, Cambridge, 1979.

    MATH  Google Scholar 

  46. K.B.Sinha, "On the theorem of M.G.Krein", Univ. Geneva preprint, 1975.

    Google Scholar 

  47. M. Stone, Ann. Phys. 155 (1984), 56–84.

    CrossRef  ADS  Google Scholar 

  48. E.C. Titchmarsh, "Eigenfunction Expansions associated with Second-Order Differential Equations II", Clarendon Press, Oxford, 1958.

    MATH  Google Scholar 

  49. J. Weidmann, Math. Z. 98 (1967), 268–302; 180 (1982), 423–427.

    CrossRef  MathSciNet  Google Scholar 

  50. E. Witten, Nucl. Phys. B202 (1982), 253–316.

    CrossRef  ADS  Google Scholar 

  51. V.A. Zheludev, Topics in Math. Phys. 4 (1971), 55–75.

    Google Scholar 

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Gesztesy, F. (1986). Scattering theory for one-dimensional systems with nontrivial spatial asymptotics. In: Balslev, E. (eds) Schrödinger Operators, Aarhus 1985. Lecture Notes in Mathematics, vol 1218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073045

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  • DOI: https://doi.org/10.1007/BFb0073045

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