Integral Equations and Operator Theory

, Volume 58, Issue 4, pp 563–571

Schrödinger Operators with Rapidly Oscillating Potentials


DOI: 10.1007/s00020-007-1501-5

Cite this article as:
Sasaki, I. Integr. equ. oper. theory (2007) 58: 563. doi:10.1007/s00020-007-1501-5


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 35J10Secondary 35P15


Oscillating potentialLieb-Thirring inequality

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan