  Making use of recent techniques in the theory of selfadjoint extensions of
symmetric operators, we characterize the class of point interaction
Hamiltonians in a 3-D bounded domain with regular boundary. In the particular
case of one point interaction acting in the center of a ball, we obtain an
explicit representation of the point spectrum of the operator togheter with the
corresponding related eigenfunctions. These operators are used to build up a
model-system where the dynamics of a quantum particle depends on the state of a
quantum bit.
