Skip to main content
SpringerLink
Log in

Scattering theory for one-dimensional systems with nontrivial spatial asymptotics

  • Conference paper
  • First Online:
Schrödinger Operators, Aarhus 1985

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  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.

    Book  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.

    Article  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.

    Article  ADS  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  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.

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  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.

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  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.

    Chapter  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Graz, A-8010, Graz, Austria

    F. Gesztesy

Authors
  1. F. Gesztesy
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Erik Balslev

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16826-3

  • Online ISBN: 978-3-540-47119-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation