MARTINEZ Andre'
On a General Born--Oppenheimer Reduction Scheme
(28K, LATeX 2e)
ABSTRACT. We perform a general reduction scheme that can be applied in particular
to the spectral study of operators of the type $P=P(x,y,hD_x,D_y)$ as
$h$ tends
to zero. This scheme permits to reduce the study of
$P$ to the one of a semiclassical matrix operator of the type
$A=A(x,hD_x)$. Here, for any fixed
$(x,\xi )\in\R^n$, the eigenvalues of the principal symbol $a(x,\xi )$
of $A$ are eigenvalues of the operator $P(x,y,\xi ,D_y)$.