  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 Schr\"{o}dinger 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.
