State-space trajectories in classical mechanics can be used to nicely represent the time evolution of a given system. In the case of the harmonic oscillator, for instance, we get ellipses. How does this situation carry over to quantum mechanics? Can the time evolution of, say, the quantum harmonic oscillator be represented by some 'trajectory' in Hilbert space? The obtained wave functions do not seem to lend themselves for such 'elegant' representations.