Skip to main content

Moving Potentials and the Completeness of Wave Operators. Part II: Propagating Observables on Scattering States

  • Chapter
Order,Disorder and Chaos in Quantum Systems

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 46))

  • 171 Accesses

Abstract

The paper is devoted to the time evolution of the position and impulse operators as well as certain functions of them, for example the dilation and classical kinetic energy operator, in quantum mechanical scattering theory with time-dependent and travelling along fixed trajectories long range potentials.

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 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

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. Amrein,W.O.; Georgescu,V.: On the characterization of bounded states and scattering states in quantum mechanics, Helv. Phys. Acta 46 (1973), 653–657.

    Google Scholar 

  2. Enss,V.: Asymptotic observables on scattering states, Commun. Math. Phys. 89(1983), 245–268.268.

    Google Scholar 

  3. Kato, T.: Perturbation theory for linear operators, Springer -Verlag, Berlin-Heidelberg-New York, 1966.

    Google Scholar 

  4. Kitada,H,; Yajima,K.: A scattering theory for time-dependent long-range potentials, Duke Math. J. 49 (1982), 341–376.

    Article  Google Scholar 

  5. Kitada,H.; Yajima,K.: Remarks on our paper “A scattering theory for time-dependent long-range potentials”, Duke Math. J. 50 (1983), 1005–1016.

    Article  Google Scholar 

  6. Neidhardt,H.: Moving potentials and the completeness of wave operators. Part I: The propagator, in preparation.

    Google Scholar 

  7. Neidhardt,H.: Moving potentials and the completeness of wave operators. Part III: Existence and completeness, in preparation.

    Google Scholar 

  8. Reed,M.; Simon,B.: Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972.

    Google Scholar 

  9. Ruelle,D.: A remark on bounded states in potential scattering theory, Nuovo Cimento 59A (1969), 655–662.

    Google Scholar 

  10. Yafaev,D.R.: Asymptotic completeness for the multidimensional time-dependent Schrödinger equation, Dokl. Akad. Nauk SSSR 21 (1980), 545–549.

    Google Scholar 

  11. Yajima,K.: A multiple-channel scattering theory for some time-dependent Hamiltonians, charge transfer problems, Commun. Math. Phys. 75 (1980), 153–178.

    Article  Google Scholar 

  12. Yajima,K.: Existence of solutions for Schrödinger evolution equations, Commun. Math. Phys. 110 (1987), 415–426.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Birkhäuser Verlag Basel

About this chapter

Cite this chapter

Neidhardt, H. (1990). Moving Potentials and the Completeness of Wave Operators. Part II: Propagating Observables on Scattering States. In: Exner, P., Neidhardt, H. (eds) Order,Disorder and Chaos in Quantum Systems. Operator Theory: Advances and Applications, vol 46. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7306-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7306-2_12

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7308-6

  • Online ISBN: 978-3-0348-7306-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics