  Consider the Schrodinger equation -\Delta u =(k+V) u in an infinite slab S=
\R^{n-1}x (0,1), where V is a bounded potential supported on a set D of finite
measure. We prove necessary conditions for the existence of nontrivial
admissible solutions. These conditions involve the sup. of |V|, the measure of
D, and the distance of k from the "special set" {\pi^2 m^2, m positive
integer}. In many cases, these inequalities are sharp.
