Skip to main content
SpringerLink
Log in

On Schrödinger operators with von Neumann-Wigner type potentials

  • Conference paper
  • First Online:
Differential Equations and Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1285))

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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. Agmon, S.: Spectral properties of Schrodinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa Sci. Mat. (1975), 151–218.

    Google Scholar 

  2. Benz-Artzi, M. and Devinatz, A.: Spectral and scattering theory for the adiabatic oscillator and related potentials, J. Math. Phys. 111(1979), 594–607.

    Article  MathSciNet  MATH  Google Scholar 

  3. Devinatz, A. and Rejto, P.: A limiting absorption principle for Schrodinger operators with oscillating potentials. I.J. Diff. Equations. 49, (1983), 85–104.

    Article  MathSciNet  MATH  Google Scholar 

  4. Devinatz, A. and Rejto, P.: A Limiting absorption Principle for Schrodinger operators with oscillating potentials. II. J. Diff. Equations. 49, (1983), 85–104.

    Article  MathSciNet  MATH  Google Scholar 

  5. Erdelyi, A.: Asymptotic Expansions. Dover, New York, 1956.

    MATH  Google Scholar 

  6. Pauli Lectures on Physics, Vol. 5, Wave Mechanics, Enz, C., P., (Ed.), MIT Press, Cambridge, Mass. 1977, See Sect. 27, The WKB-method.

    Google Scholar 

  7. Jager, W. and Rejto, P.: On the absolute continuity of the spectrum of Schrodinger operators with long range potentials. Oberwolfach Tagungsberichte, 17.7.-23.7. 1977.

    Google Scholar 

  8. Jager, W. and Rejto, P.: Limiting absorption principle for some Schrodinger operators with exploding potentials I. J. Math. Anal. Appl. 91(1983), 192–228.

    Article  MathSciNet  MATH  Google Scholar 

  9. Jager, W. and Rejto, P.: Limiting absorption principle for some Schrodinger operators with exploding potentials II. J. Math. Anal. Appl. 95 (1983), 169–194.

    Article  MathSciNet  MATH  Google Scholar 

  10. Kato, T.: Perturbation Theory for Linear Operators, Springer-Verlag, 1973.

    Google Scholar 

  11. Langer, R.E.: The asymptotic solutions of ordinary linear differential equations for the second order with special reference to a turning point. Trans. Amer. Math. Soc. 67 (1949), 461–490.

    Article  MathSciNet  MATH  Google Scholar 

  12. Mochizuki, M., and Uchiyama, J.: Radiation conditions and spectral theory for 2-body Schrodinger operators with “oscillating” long range potentials I. J. Math. Kyoto Univ. 18(2) (1978), 377–408.

    MathSciNet  MATH  Google Scholar 

  13. Reed. M., and Simon, B.: Analysis of operators, Methods of Modern Mathematical Physics. Vol. IV, Academic Press. 1978, Section XIII.13, Example 1.

    Google Scholar 

  14. Saito, Y.: On the asymptotic behavior of the solutions of the Schrodinger equation. Osaka. J. Math. 14 (1977), 11–35. See the Ricatti equation (3.11).

    MathSciNet  MATH  Google Scholar 

  15. Saito, Y.: Schrodinger Operators with a nonspherical radiation condition, to appear.

    Google Scholar 

  16. Saito, Y.: These Proceedings.

    Google Scholar 

  17. von Neumann, J. and Wigner, E.: Über merkwurdige diskrete Eigenwerte. Phys. Zschr 30(1929), 465–467.

    MATH  Google Scholar 

  18. Olver, F., T.,W.: Asymptotics and Special Functions. Academic Press. 1974.

    Google Scholar 

  19. Wasov, W.: Asymptotic Expansions for Ordinary Differential Equations. Wiley-Interscinec, 1965.

    Google Scholar 

  20. Devinatz, A., Moeckel, R., and Rejto, P.: A Wronskian Estimate For Schrodinger Operators With von Neumann-Wigner Type Potentials. Univ. Minn. Math. Report 1986.

    Google Scholar 

  21. Atkinson, F.: Discrete and Continuous Boundary Problems, Academic Press 1964, See Theorem 88.1.

    Google Scholar 

  22. Atkinson, F.: The asymptotic solutions of second order differential equations, Ann. Mat. Pura Appl. 37 (1954), 347–378.

    Article  MathSciNet  MATH  Google Scholar 

  23. Isozaki, Hiroshi: On the generalized Fourier transform associated with Schrodinger operators with long-range perturbations. J. reine angewandte Math. 337 (1982), 18–67.

    MathSciNet  MATH  Google Scholar 

  24. Reed, M. and Simon, B.: Scattering Theory. Methods of Modern Mathematical Physics Vol. III, Academic Press 1979. See Section XI.8 and the notes to it where references to the original works of Natveev-Skriganov, Combescure-Ginibre and Schechter are also given.

    Google Scholar 

  25. Harris, W.A. and Lutz, D.A. A unified theory of asymptotic integration. J. Math. Anal. Appl. 57 (1977), 571–586.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Northwestern University, 60201, Evanston, Illinois

    Allen Devinatz

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, Minnesota

    Richard Moeckel

  3. School of Mathematics, University of Minnesota, 55455, Minneapolis, Minnesota

    Peter Rejto

Authors
  1. Allen Devinatz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard Moeckel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Rejto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ian W. Knowles Yoshimi Saitō

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Devinatz, A., Moeckel, R., Rejto, P. (1987). On Schrödinger operators with von Neumann-Wigner type potentials. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080584

Download citation

  • DOI: https://doi.org/10.1007/BFb0080584

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18479-9

  • Online ISBN: 978-3-540-47983-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation