  We discuss an extension of the generator coordinate method (GCM) by taking
simultaneously a collective coordinate and its conjugate momentum as generator
coordinates. To this end, we follow the idea of the dynamical GCM (DGCM)
proposed by Goeke and Reinhard. We first show that the DGCM method can be
regarded as an extension of the double projection method for the center of mass
motion. As an application of DGCM, we then investigate the particle number
projection, for which we not only carry out an integral over the gauge angle as
in the usual particle number projection but also take a linear superposition of
BCS states which have different mean particle numbers. We show that the ground
state energy is significantly lowered by such effect, especially for magic
nuclei for which the pairing gap is zero in the BCS approximation. This
suggests that the present method makes a good alternative to the variation
after projection (VAP) method, as the method is much simpler than the VAP.
