  We study the action of the free quantum Hamiltonian in the Schr\"odinger
representation on functional spaces generated by Gaussian states with boundary
conditions set by localized external sources. It turns out that inspite of very
general initial assumptions the proposed scheme requires at least two sources
at a distance limited by non-zero constant of the model. In this way we provide
example of quntum field evolved by the action of the free Hamiltonian confining
external sources which set boundary conditions.
