  We present a minisuperspace analysis of a class of Lorentzian wormholes that
evolves quantum mechanically in a background Friedman Robertson Walker
spacetime. The quantum mechanical wavefunction for these wormholes is obtained
by solving the Wheeler-DeWitt equation for Einstein gravity on this
minisuperspace. The time-dependent expectation value of the wormhole throat
radius is calculated to lowest order in an adiabatic expansion of the
Wheeler-DeWitt hamiltonian. For a radiation dominated expansion, the radius is
shown to relax asymptotically to obtain a value of order the Planck length
while for a deSitter background, the radius is stationary but always larger
than the Planck length. These two cases are of particular relevance when
considering wormholes in the early universe.
