Integral Equations and Operator Theory

, Volume 58, Issue 4, pp 563–571 | Cite as

Schrödinger Operators with Rapidly Oscillating Potentials



Schrödinger operators \(\hat{H} = -\Delta + V\) with rapidly oscillating potentials V such as \(cos |x|^{2}\) are considered. Such potentials are not relatively compact with respect to the free Schrödinger operator −Δ. We show that the oscillating potential V do not change the essential spectrum of −Δ. Moreover we derive upper bounds for negative eigenvalue sums of Ĥ.

Mathematics Subject Classification (2000).

Primary 35J10 Secondary 35P15 


Oscillating potential Lieb-Thirring inequality 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan

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