Page "Quantum mechanics" Paragraph 28

Wave functions change as time progresses.

The Schrödinger equation describes how wavefunctions change in time, playing a role similar to Newton's second law in classical mechanics.

The Schrödinger equation, applied to the aforementioned example of the 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 with time.

This also has the effect of turning a position eigenstate ( which can be thought of as an infinitely sharp wave packet ) into a broadened wave packet that no longer represents a ( definite, certain ) position eigenstate.