Boundary dynamics and topology change in quantum mechanics

Abstract

We show how to use boundary conditions to drive the evolution on a quantum mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schrödinger 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 the topology change and to obtain necessary conditions to accomplish it in a dynamical way.