- 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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97-509.tex