97-509 Helffer B., Mohamed A.
Asymptotic of the Density of States for the Schr\"odinger Operator with Periodic Electric Potential (131K, LATEX) Sep 18, 97
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Abstract. We analyze in this article the spectral properties of the Schr\"odinger operator with periodic potential on L^2(\rz^n). It is proven that the integrated density of states N(\mu) has an asymptotic expansion of the form N(\mu) =a_n \mu^{n/2}+a_{n-2} \mu^{\frac{n-2}{2}}+O(\mu^{(n-3+\epsilon)/2}), for all \epsilon >0. This gives also a proof of the Bethe-Sommerfeld conjecture for n<5.

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