  The properties of vortex states in a Bose-Einstein condensed cloud of atoms
are considered at zero temperature. Using both analytical and numerical methods
we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud
of atoms containing a vortex is released from a trap. In two dimensions we find
the simple result that the time dependence of the cloud radius is given by
$(1+\omega^2t^2)^{1/2}$, where $\omega$ is the trap frequency. We calculate and
compare the expansion of the vortex core and the cloud radius for different
numbers of particles and interaction strengths, in both two and three
dimensions, and discuss the circumstances under which vortex states may be
observed experimentally.
