Schrödinger Operators with Oscillating Potentials

  • Allen Devinatz
  • Peter Rejto


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,
$${P_o}\left( x \right) = c\frac{{\sin b{{\left| x \right|}^\alpha }}}{{{{\left| x \right|}^\beta }}},\alpha ,\beta > 0$$
where c = -8, b = 2 and α = β = 1.


Compact Interval Schwarzian Derivative Short Range Potential Asymptotic Completeness Pioneer Contribution 
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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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