Other Mathematics Commons^™

Green's Function For The Schrodinger Equation With A Generalized Point Interaction And Stability Of Superoscillations, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study the time dependent Schrödinger equation with all possible self-adjoint singular interactions located at the origin, which include the δ and δ'-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability …