Continuum limit for scattering solutions to discrete Schrödinger equations

Emeritus Professor Hiroshi Isozaki (University of Tsukuba)
04.03.2019, Exactum C124, 2pm-4pm


We show that solutions to the Schrödinger $(-\Delta + V(x) - E) uf $ in Rd, where V(x) is a real compactly supported potential and E > 0 is a constant, satisfying the radiation condition is approximated by solutions to discrete Schrödinger equations on the periodic lattice $Zhd$  when the mesh size h goes to 0.