  We generalize the Gutzwiller approximation scheme to the calculation of
nontrivial matrix elements between the ground state and excited states. In our
scheme, the normalization of the Gutzwiller wave function relative to a
partially projected wave function with a single non projected site (the
reservoir site) plays a key role. For the Gutzwiller projected Fermi sea, we
evaluate the relative normalization both analytically and by variational
Monte-Carlo (VMC). We also report VMC results for projected superconducting
states that show novel oscillations in the hole density near the reservoir
site.
