Méthode BKW formelle et spectre des molécules polyatomiques dans l'approximation de Born Oppenheimer

Abstract

We studied the spectrum of P D −h21x − 1y C V .x; y/ on L2 ð€€€ IR3n x IR3p y

; when h tends to zero; n 2; p 2 IN ; in the case where the potential V .x; y/ is singular and of Coulomb type and the first eigenvalue of Q.x/ D−1y C V .x; y/ on L ð€€€ IR3p y

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: