Class of Potentials with Extremely Narrow Resonances. I. Case with Discrete Rotational Symmetry.

摘要

We consider a quantum-mechanical particle in three dimensions, subject to point interactions (Fermi pseudopotentials) placed on the vertices of a regular plane polygon. If N, the number of vertices, tends to infinity and the distance between two consecutive interaction centers tends to a constant, we show that our system has resonances that tend exponentially fast to the real axis. We discuss several conjectures on the generality of this result and stress its relevance as a simplified model for the Yagi-Uda antenna array of classical electromagnetism. (Atomindex citation 13:660150)