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.