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For the understanding of surface effects it is useful to consider the motion of particles in domains with position-dependent -boundary conditions. In the one-dimensional case it has been shown that the operator H = —d 2/dx 2 with boundary conditions. = q(0), q € R, is the norm resolvent limit of —d 2/dx2 ± nV(nx) with Neumann boundary conditions for n -* oc, where V is an L 1 -function satisfying

On the Spectrum of Schrödinger Operators at the Half Space with a Certain Class of Boundary Conditions