Dispersive estimate for the Schroedinger equation with point interactions
Abstract
We consider the Schroedinger operator in R3 with N point interactions placed at Y=(y1, ... ,yN), yj in R3, of strength a=(a1, ... ,aN). Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove a (weighted) dispersive estimate for the corresponding Schroedinger flow. In the special case N=1 the proof is directly obtained from the unitary group which is known in closed form.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.