Skip to main content
SpringerLink
Log in

Resonance Phenomenon for Potentials of Wigner–von Neumann Type

  • Conference paper
  • First Online:
Geometric Methods in Physics

Part of the book series: Trends in Mathematics ((TM))

Abstract

The paper discusses the behavior of solutions of the second-order differential equations possessing a resonance effect known for the Wigner–von Neumann potential. A class of potentials generalizing that of Wigner–von Neumann is presented.

Mathematics Subject Classification (2010). Primary 34E10; Secondary 34F15.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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. D.B. Hinton, M. Klaus, J.K. Shaw, Embedded half-bound states for potentials of Wigner–von Neumann type, Proc. London Math. Soc. (3) 62 (1991), no. 3, 607–646.

    Google Scholar 

  2. M.S.P. Eastham, H. Kalf, Schrödinger-type operators with continuous spectra (1982).

    Google Scholar 

  3. A. Wintner, Asymptotic integration of the adiabatic oscillator Amer. Journ. Math., vol. 69 (1947), pp. 251–272.

    Article  MathSciNet  MATH  Google Scholar 

  4. W.A. Harris, D.A. Lutz, Asymptotic integration of adiabatic oscillator Amer. Journ. Math. Anal. Appl. 51 (1975), 76–93.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Białystok, Akademicka 2, PL-15-267, Bia–ystok, Poland

    Barbara Pietruczuk

Authors
  1. Barbara Pietruczuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Barbara Pietruczuk .

Editor information

Editors and Affiliations

  1. Departamento de Física, CINVESTAV, Mexico City, Distrito Federal, Mexico

    Piotr Kielanowski

  2. Dept. of Mathematics and Statistics, Concordia University, Montreal, Québec, Canada

    S. Twareque Ali

  3. Department of Mathematics - MC J415, Brock University, St. Catharines, Ontario, Canada

    Alexander Odesskii

  4. Institute of Mathematics, University of Bialystok, Bialystok, Poland

    Anatol Odzijewicz

  5. Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

    Martin Schlichenmaier

  6. School of Mathematics, University of Manchester, Manchester, United Kingdom

    Theodore Voronov

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Basel

About this paper

Cite this paper

Pietruczuk, B. (2013). Resonance Phenomenon for Potentials of Wigner–von Neumann Type. In: Kielanowski, P., Ali, S., Odesskii, A., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0645-9_19

Download citation

Publish with us

Policies and ethics

Search

Navigation