  We consider time-dependent relaxation of observables in quantum systems of
chaotic and regular type. We show that the spread of the wave function in the
Hilbert space is determined by the survival probability which is known to have
pre-exponential, exponential, and long-term power-law limiting behaviors. This
result relies on complexity of the wave functions and thus is generic to many
systems. In the chaotic limit modeled by the Gaussian Orthogonal Ensemble we
show that the survival probability obtained analytically also fully defines the
relaxation timescale of observables. This is not the case in general, using
realistic nuclear shell model and the quadrupole moment as an observable we
demonstrate that the relaxation time is significantly longer than defined by
the survival probability of the initial state. An example of the non-chaotic
limit of coherent and squeezed states provides an additional illustration.
