**Abstract: **
Making use of the theory of selfadjoint extensions of symmetric operators,
we give a general characterization of point interaction potentials acting in
a bounded domain of R^3. In particular we show that singular perturbations
of the Laplacian ,in bounded domains, can produce a global variation of its
spectrum.
We use these results to describe a gas of particles interacting with a q-bit
through a confining delta potential. This would represent a model for the
mathematical description of a quantum measurement process where the spin is
measured through the observation of the particles density.