Abstract
Consider the Schrodinger equation -Δu =(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" {π^2 m^2, m positive integer}. In many cases, these inequalities are sharp.
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