University of Illinois at Chicago
On confining potentials and essential self-adjointness for Schrödinger operators
Abstract: We consider a Schrödinger operator on a bounded domain in R^n, and search for optimal growth criteria for the potential close to the boundary of the domain insuring essential self-adjointness of the associated operator. We find an abstract integral criterion for the potential, from which we prove that one can add optimal logarithmic type corrections to the classical criteria. As a consequence of our method, we study the question of confinement of spinless and spin 1/2 quantum particles on the unit disk in R, and achieve magnetic confinement solely by means of the growth of the magnetic field.
Friday October 26, 2012 at 3:00 PM in SEO 636