  We study the collapse and revival of interference patterns in the momentum
distribution of atoms in optical lattices, using a projection technique to
properly account for the fixed total number of atoms in the system. We consider
the common experimental situation in which weakly interacting bosons are loaded
into a shallow lattice, which is suddenly made deep. The collapse and revival
of peaks in the momentum distribution is then driven by interactions in a
lattice with essentially no tunnelling. The projection technique allows to us
to treat inhomogeneous (trapped) systems exactly in the case that
non-interacting bosons are loaded into the system initially, and we use
time-dependent density matrix renormalization group techniques to study the
system in the case of finite tunnelling in the lattice and finite initial
interactions. For systems of more than a few sites and particles, we find good
agreement with results calculated via a naive approach, in which the state at
each lattice site is described by a coherent state in the particle occupation
number. However, for systems on the order of 10 lattice sites, we find
experimentally measurable discrepancies to the results predicted by this
standard approach.
