Skip to main content

Coupled-Channel Marchenko Inversion in One Dimension with Thresholds

  • Conference paper
Inverse and Algebraic Quantum Scattering Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 488))

Abstract

The one-dimensional coupled-channel Marchenko equation in the presence of thresholds is derived. Various aspects of this equation are discussed and a numerical algorithm for its solution is proposed. The efficiency of the algorithm is demonstrated using simulated scattering data.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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

  • Agranovich Z. S. and Marchenko V.A. (1963), The Inverse Problem in Scattering Theory, Gordon and Breach, New York.

    Google Scholar 

  • Anderson E. et al. (1992), LAPACK Users Guide, SIAM, Philadelphia.

    MATH  Google Scholar 

  • Braun M., Sofianos S.A., and Lipperheide R. (1995), Inverse Problems 11, L1.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Calogero F. and Degasperis D. (1982), Spectral Transform and Solitons North-Holland, Amsterdam, Vol 1.

    Google Scholar 

  • Chadan K. and Sabatier P.C. (1982), Inverse Problems in Quantum Scattering Theory, 2nd edition, Springer, Berlin.

    Google Scholar 

  • Corvi M. (1992), Numerical Algorithms for One-Dimensional Inverse Scattering and Imaging, Bertero M. and Pike E. R., Eds., Hilger, Bristol, Philadelphia, New York, p. 411.

    Google Scholar 

  • Fiedeldey H., Lipperheide R., Leeb H. and Sofianos S.A. (1992), Phys. Lett. A179, 347.

    Article  Google Scholar 

  • Ghosh Roy D. N. (1991), Methods of Inverse Problems in Physics, CRC Press, Boston.

    Google Scholar 

  • Gudkov V. P., Opat G.I. and Klein A.G. (1994), J. Phys.: Condensed Matter 5, 9013.

    ADS  Google Scholar 

  • de Haan V. O., van Well A.A., Adenwalla S. and Fetcher G. P. (1995), Phys. Rev. B52, 10831.

    Article  Google Scholar 

  • Jordan A. K. and Ladouceur H. D. (1987), Phys. Rev. A36, 4245.

    Google Scholar 

  • Jordan A. K. and Lakshmanasamy S. (1989), J. Opt. Soc. Am. A6, 1206.

    Google Scholar 

  • Kohlhoff H. and von Geramb H.V. (1993), in Quantum Inversion: Theory and Applications, Springer, Berlin, p. 314.

    Google Scholar 

  • Lipperheide R., Reiss G., Leeb H., Fiedeldey H., and Sofianos S.A. (1995), Phys. Rev. B51, 1 1032.

    Google Scholar 

  • Lipperheide R., Fiedeldey H., Leeb H., Reiss G., and Sofianos S.A. (1995), Physica B213, 914.

    Google Scholar 

  • Lipperheide R., Reiss G., Leeb H. and Sofianos S.A. (1996), Physica B221, 514.

    Article  Google Scholar 

  • Majkrzak C.F. and Berk N. F. (1995), Phys. Rev. B52, 10827.

    Article  Google Scholar 

  • Newton R. G. and Jost R. (1955), Nuovo Cimento 1, 590.

    Article  MATH  MathSciNet  Google Scholar 

  • Pechenick K. R. and Cohen J. M. 1981, Phys. Lett. 82A, 156.

    Article  MathSciNet  Google Scholar 

  • Pechenick K. R. and Cohen J. M. (1983), J. Math. Phys. 24 (2), 406.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Press W. H., Teukolsky S. A., Vetterling W. T., and Flannery B. P. (1992), Numerical Recipes in FORTRAN 2nd edition, Cambridge University Press.

    Google Scholar 

  • Sacks P. E. (1993), Wave Motion 18, 21.

    Article  MATH  MathSciNet  Google Scholar 

  • Sivia D. S., Hamilton W.A. and Smith G. S. (1991), Physica B173, 121.

    Article  Google Scholar 

  • Wadati M. and Kamijo T. (1974), Prog. Theor. Phys. 52, 397

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Weidenmiiller H. A. (1964), Ann.Phys. (N.Y.) 29, 60.

    Article  ADS  Google Scholar 

  • Zakhariev B. N. and Suzko A.A. (1990), Direct and Inverse Problems, Springer, Berlin.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sofianos, S.A., Braun, M., Lipperheide, R., Leeb, H. (1997). Coupled-Channel Marchenko Inversion in One Dimension with Thresholds. In: Apagyi, B., Endrédi, G., Lévay, P. (eds) Inverse and Algebraic Quantum Scattering Theory. Lecture Notes in Physics, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-14145-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-14145-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-14147-2

  • Online ISBN: 978-3-662-14145-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics