Méthode BKW formelle et spectre des molécules polyatomiques dans lapproximation de Born-Oppenheimer

We studied the spectrum of P = -h2Dx - Dy + V (x,y) on L2(IRx3n × IRy3p), when h tends to zero, n >=2, p E IN*, in the case where the potential V(x,y) is singular and of Coulomb type and the first eigenvalue of Q (x) = -Dy + V(x,y) on L (IRy3p) admits an unbounded well. Using a formal version of the h-pseudodifferential calculus on the regularized operator of P with adapted changes, we obtained WKB-type expansions of eigenvalues and associated eigenfunctions of P.