Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques

Robert, Didier; Helffer, Bernard

Annales de l'Institut Fourier, Tome 31 (1981) no. 3, pp. 169-223

Dans cet article nous généralisons les résultats obtenus par J. Chazarain sur le spectre d’opérateurs de Schrödinger $P\left(h\right)=\frac{h^2}{2}\Delta +V$ lorsque $h\to 0$. Nous étendons ses résultats aux opérateurs pseudo-différentiels globalement elliptiques d’ordre $m>0$.

In this article we extend results obtained by J. Chazarain about the spectrum of Schrödinger operators: $P\left(h\right)=\frac{h^2}{2}\Delta +V$ when $h>0$ approach 0. We obtain the same results for globally elliptic pseudodifferential operators of order $m>0$.

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