Peter Kuchment and Boris Vainberg
On absence of embedded eigenvalues for Scr\"{o}dinger operators 
with perturbed periodic potentials
(40K, LATEX)

ABSTRACT.   The problem of absence of eigenvalues imbedded into the continuous spectrum 
is considered for a Schr\"{o}dinger operator with a periodic potential 
perturbed by a sufficiently fast decaying ``impurity'' potential. Results of 
this type have previously been known for the one-dimensional case only. Absence 
of embedded eigenvalues is shown in dimensions two and three if the 
corresponding Fermi surface is irreducible modulo natural symmetries. It is 
conjectured that all periodic potentials satisfy this condition. Separable 
periodic potentials satisfy it, and hence in dimensions two and three 
Schr\"{o}dinger operator with a separable periodic potential perturbed by a 
sufficiently fast decaying ``impurity'' potential has no embedded eigenvalues.