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Schrödinger Operators with Oscillating Potentials

  • Allen Devinatz
  • Peter Rejto

Abstract

Dae to the pioneering contributions of Kato-Kuroda [10], [11] and to the more recent works of Agmon [l] and Enss [6], a spectral and scattering theory for Schrodinger operators with short range potentials is now well established. An interesting example of a potential which does not belong to this class is the Wigner-von- Neumann [17] potential. This potential is the sum of a short range potential and of an oscillating one which is of the form,
$${P_o}\left( x \right) = c\frac{{\sin b{{\left| x \right|}^\alpha }}}{{{{\left| x \right|}^\beta }}},\alpha ,\beta > 0$$
(1.1)
where c = -8, b = 2 and α = β = 1.

Keywords

Compact Interval Schwarzian Derivative Short Range Potential Asymptotic Completeness Pioneer Contribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Allen Devinatz
    • 1
  • Peter Rejto
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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