B. Messirdi, A. Senoussaoui 
Resonances for a General Hamiltonian in the Born-Oppenheimer Approximation
(221K, LaTeX 2e)

ABSTRACT.  We study the discrete spectrum of a 
general class of Born-Oppenheimer Hamiltonians of the type: 
\begin{equation*} 
H=-h^{2}\Delta _{x}+P\left( x,y,D_{y}\right) \text{ on }L^{2}\left( \mathbb{R% 
}_{x}^{n}\times \mathbb{R}_{y}^{p}\right) ,n,p\in \mathbb{N}^{\ast } 
\end{equation*}% 
{\small when }$h${\small \ tends to }$0^{+}${\small , here }$P\left( 
x,y,D_{y}\right) ${\small \ is a pseudodifferential operator on }$% 
L^{2}\left( \mathbb{R}_{y}^{p}\right) .$ {\small In the case where the first 
eigenvalue }$\lambda _{1}\left( x\right) ${\small \ of }$P\left( 
x,y,D_{y}\right) ${\small \ on }$L^{2}\left( \mathbb{R}_{y}^{p}\right) $% 
{\small \ admits one non degenerate point-well, we obtain WKB-type 
expansions for all order in }${\small h}^{{\small 1/2}}${\small \ of 
eigenvalues (in the interval }$[0,C_{0}h],${\small \ }$C_{0}>0)${\small \ 
and associated normalized eigenfunctions of }$H,${\small \ and this for all 
orders in }$h^{1/2}$.