07-116 O. Safronov and B. Vainberg

Eigenvalue estimates for random Schr\"odinger operators (157K, pdf) May 9, 07

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Abstract. In this paper we study the negative eigenvalues $\lambda_j$ of the Schr\"odinger operator $-\Delta-V(x)$. We prove that $\sum_j|\lambda_j|^\gamma$ converges for random $L^{d+2\gamma}$-potentials with probability 1. One of the important assumptions in our paper is that the expectation of $V(x)$ is zero at every point $x$.

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