Time Evolution of the Wave Packet

• Suppose one measures the position and velocity of a particle at one time - each has some uncertainty

• What happens at later times?

• The wave packet spreads out!.

Time

One particle has probability

of being found in a range of

positions and velocities

At a later time:

Range of probable

positions spreads out in

time because of spread

in velocities

Range of probablevelocity around an

average

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