Skip to main content
SpringerLink
Log in

Constructive scattering theory

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider a problem of factoring the scattering matrix for Schrödinger equation on the real axis. We find the elementary factorization blocks in both the finite and infinite cases and establish a relation to the matrix conjugation problem. We indicate a general scheme for constructing a large class of scattering matrices admitting a quasirational factorization.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. B. Shabat, “Difference Schrödinger equation and quasisymmetric polynomials,” Theor. Math. Phys., 184, 1067–1077 (2015).

    Article  MATH  Google Scholar 

  2. A. B. Shabat, “Scattering theory for delta-type potentials,” Theor. Math. Phys., 183, 540–552 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  3. A. B. Shabat, “Inverse spectral problem for delta potentials,” JETP Lett., 102, 620–623 (2015).

    Article  ADS  Google Scholar 

  4. P. Koosis, The Logarithmic Integral: I (Cambridge Stud. Adv. Math., Vol. 12), Cambridge Univ. Press, Cambridge (1997).

    MATH  Google Scholar 

  5. V. Bargman, “Remarks on the determination of a central field of force from the elastic scattering phase shifts,” Phys. Rev., 75, 301–303 (1949).

    Article  ADS  MathSciNet  Google Scholar 

  6. A. B. Shabat, “Rational interpolation and solitons,” Theor. Math. Phys., 179, 637–648 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Sh. Badakhov and A. B. Shabat, “Darboux transformations in the inverse scattering problem,” Ufa Math. Journal, 8, No. 4, 42–51 (2016).

    Article  MathSciNet  Google Scholar 

  8. R. Ch. Kulaev and A. B. Shabat, “Inverse Scattering problem for finite potentials in the space of Borel measures [in Russian],” Preprint, SMI VSC RAS, Vladikavkaz (2016).

    Google Scholar 

  9. A. B. Shabat, “Functional Cantor equation,” Theor. Math. Phys., 189, 1712–1717 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. B. Shabat, “Inverse-scattering problem for a system of differential equations,” Funct. Anal. Appl., 9, 244–247 (1975).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Moscow, Russia

    A. B. Shabat

Authors
  1. A. B. Shabat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. B. Shabat.

Additional information

This research is supported by a grant from the Russian Science Foundation (Project No. 15-11-20007).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shabat, A.B. Constructive scattering theory. Theor Math Phys 193, 1420–1428 (2017). https://doi.org/10.1134/S0040577917100026

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577917100026

Keywords

Search

Navigation