VALEURS PROPRES ET RESONANCES DES MOLECULES POLYATOMIQUES DANS L'APPROXIMATION DE BORN-OPPENHEIMER1

Abstract

We study the spectrum of Schrodinger operator P (h) for a polyatomic molecul in the Born-Oppenheimer approximation where the mass ratio h2 of electronic to nuclear mass tends to zero. We prove that this study can be reduced to the one of a semi-classical pseudo-differential operator and we obtain WKB-type expansion of eigenvalues, resonaces and eigenfunctions of P (h) to all orders of h.