Session S30 - Mathematical Methods in Quantum Mechanics

Friday, July 16, 19:00 ~ 19:25 UTC-3

A functional model for symmetric operators and its applications to spectral theory

Luis O. Silva

Universidad Nacional Autónoma de México, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

This talk introduces a functional model for symmetric operators based on the representation theory developed by Krein and Strauss. Such model allows one to make use of results and techniques in de Branges space and the moment problem theories to study the spectral properties of the selfadjoint extensions of a given symmetric operator. By this approach, necessary and sufficient conditions for a discrete set to be the spectrum of a singular Schrödinger operator are obtained. The stability of these conditions is studied when an eigenvalue is added to the spectrum.

Joint work with Rafael del Rio (Universidad Nacional Autónoma de México) and Julio H. Toloza (Universidad Nacional del Sur, Argentina).

View abstract PDF