, Volume 58, Issue 4, pp 563-571
Date: 27 Jun 2007

Schrödinger Operators with Rapidly Oscillating Potentials

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Abstract.

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.