Wave Packets

Since a momentum eigenstate has a precisely defined momentum, the Uncertainty Principle tells us that its position is completely uncertain; it must extend throughout all space. This is not a good model of actual particles, which are usually localized. A more useful wave function consists of a mixture of such momentum states. Since each component is a ``wave'', the resulting sum is called a ``wave packet'', and can be confined to a limited region of space. Here is a video of the time evolution of a wave packet.

YouTube Video

The packet begins as a purely real Gaussian, located on the right side of a quadratic potential well. The potential causes the packet to accelerate to the left, until it reaches the bottom of the quadratic well. It then decelerates as it moves up the left side of the well, finally stopping, and returning to the right.