- 02-407 Oleg Safronov
- The amount of discrete spectrum of a perturbed periodic Schr\"odinger
operator inside a fixed interval $(\lambda_1,\lambda_2)$
(195K, 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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