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Wave functions can change as time progresses. An equation known as the [[Schrödinger equation]] describes how wave functions change in time, a role similar to [[Newton's second law]] in classical mechanics. The Schrödinger equation, applied to our free particle, predicts that the center of a wave packet will move through space at a constant velocity, like a classical particle with no forces acting on it. However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain. This also has the effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave packets that are no longer position eigenstates.
Some wave functions produce probability distributions that are constant in time. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single [[electron]] in an unexcited [[atom]] is pictured classically as a particle moving in a circular trajectory around the [[atomic nucleus]], whereas in quantum mechanics it is described by a static, [[spherical coordinate system|spherically symmetric]] wavefunction surrounding the nucleus ([[:ImageDatoteka:HAtomOrbitals.png|Fig. 1]]). (Note that only the lowest angular momentum states, labeled ''s'', are spherically symmetric).
The time evolution of wave functions is [[determinism|deterministic]] in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a [[quantum measurement|measurement]], the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., [[random]].