In this note we prove that the essential spectrum of a Schrdinger operator with potential supported on a finite number of compact Lipschitz hypersurfaces is given by [0, +). We emphasize that the union of a family of Lipschitz hypersurfaces is in general not Lipschitz. ( 2013 WileyVCH Verlag GmbH & Co. KGaA, Weinheim)

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We consider a spinless particle coupled to a quantized Bose field and show that such a system has a ground state for two classes of short-range potentials which are alone too weak to have a zero-energy resonance.