Scattering theory for finitely many sphere interactions supported by concentric spheres

Abstract

We study stationary scattering theory for finitely many sphere interactions formally given by the Hamiltonian H=−Δ+∑j=1Nαjδ(|x|−Rj) and its generalizations to the case of interactions of the second type and interactions with nonseparated boundary conditions. In a previous publication [J. Math. Phys. 29, 660–664 (1988)], it was shown that the self-adjoint Hamiltonian H{αl},{R} corresponding to H may be defined as a limit in norm resolvent convergence of a family Hε of local scaled short-range Hamiltonians. In this paper we also study scattering theory corresponding to Hε and show that the scattering quantities associated with Hε converge to those of H{αl},{R} as ε→0.