Boundary dynamics and topology change in Quantum Mechanics

By Juan M. Pérez-Pardo (INFN, Sezione di Napoli)

In this talk we will show how one can use the boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how  this problem can be expressed in terms of the time dependent Schroedinger equation. In particular we will need the theory of self-adjoint extensions of differential operators in manifolds with boundary. An introduction of the latter as well as meaningful examples will be given.

It is known that different boundary conditions can be used to describe different topologies of the associated quantum systems. We will use the previous results to study how this topology change can be accomplished in a dynamical way.