0.002 probability density contours for a hydrogen 1s orbital, i.e., |1s|2 = 0.002 (atomic units), and for a 2pz orbital. These are stationary states; their phases are changing with time (at different rates) but the probability density is not.
. The top yellow circle is the unit circle in the complex plane for the 1s time-dependent phase factor, with the blue line indicating the phase. The lower yellow circle shows the phase factor of the 2pz orbital, for which the phase rotates at 1/4 of the speed of the 1s phase. This is a non-stationary state, in which the probability density changes with time, as do the probabilities for measuring many quantities. However, a measurement of energy will find the 1s and 2pz energies with probabilities 1/4 and 3/4 respectively, independent of time, This is because energy is a constant of the motion, as are other observables whose operators commute with the Hamiltonian.