02-406 Oleg Safronov
The amount of discrete spectrum of a perturbed periodic Schr\"odinger operator inside a fixed interval $(\lambda_1,\lambda_2)$ (193K, Postscript) Sep 30, 02
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Abstract. In this paper we extend the results of \cite{Sa} for a more general class of perturbations. Let $A$ be a periodic Schr\"odinger operator and let $V\geq0$ be a decaying potential. We study the number $\tilde{N}(\alpha)$ of the eigenvalues of the operator $A(\alpha)=A-\alpha V$ inside a fixed interval $(\lambda_1,\lambda_2)$. We obtain an asymptotic formula for $\tilde{N}(\alpha)$ as $\alpha\to\infty$.

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