  In this paper, we derive equations of motion for the normal-order, the
symmetric-order and the antinormal-order quantum characteristic functions,
applicable for general Hamiltonian systems. We do this by utilizing the
`characteristic form' of both quantum states and Hamiltonians. The equations of
motion we derive here are rather simple in form and in essence, and as such
have a number of attractive features. As we shall see, our approach enables the
descriptions of quantum and classical time evolutions in one unified language.
It allows for a direct comparison between quantum and classical dynamics,
providing insight into the relations between quantum and classical behavior,
while also revealing a smooth transition between quantum and classical time
evolutions. In particular, the $\hbar\to 0$ limit of the quantum equations of
motion instantly recovers their classical counterpart. We also argue that the
derived equations may prove to be very useful in numerical simulations.
