On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators (Q1419689)

Summary: We study spectral and scattering properties of the Laplacian \(H^{(\sigma)} = -\Delta\) in \(L_2(\mathbb{R}^2_+)\) corresponding to the boundary condition \(\frac{\partial u}{\partial\nu} + \sigma u = 0\) for a wide class of periodic functions \(\sigma\). The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators \(W_\pm(H^{(\sigma)},H^{(0)})\) exist.