  A unitary quantum gas is a gas of quantum particles with a binary interaction
of infinite scattering length and negligible range. It has been produced in
recent experiments with gases of fermionic atoms by means of a Feshbach
resonance. Using the Fermi pseudo-potential model for the atomic interaction,
we show that the time evolution of such a gas in an isotropic three-dimensional
time dependent harmonic trap is exactly given by a gauge and scaling transform.
