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Integral Equations and Operator Theory

, Volume 5, Issue 1, pp 18–49 | Cite as

A stationary approach to the existence and completeness of long-range wave operators

  • Teruo Ikebe
  • Hiroshi Isozaki
Article

Abstract

The modified wave operators intertwining the Schrödinger operators − Δ and − Δ + V(x), where V(x) is a real long-range potential, are shown to exist and to be complete. The method employed is entirely stationary (time-independent) : One constructs complete stationary wave operators, utilizing a spectral representation (eigenfunction expansion) theory, and then shows that the time-dependent modified wave operators exist and are equal to the stationary ones already constructed.

Keywords

Stationary Approach Spectral Representation Stationary Wave Modify Wave Wave Operator 
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Copyright information

© Birkhäuser Verlag 1982

Authors and Affiliations

  • Teruo Ikebe
    • 1
  • Hiroshi Isozaki
    • 1
  1. 1.Department of MathematicsKyoto UiversityKyotoJapan

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