  For time-dependent systems the wavefunction depends explicitly on time and it
is not a pure state of the Hamiltonian. We construct operators for which the
above wavefunction is a pure state. The method is based on the introduction of
conserved quantities $Q$ and the pure states are defined by ${\hat
Q}\psi=q\psi$. The conserved quantities are constructed using parametrised
mechanics and the Noether theorem.
