## Free Particle Exercise #3

 x0 = (Dx)2 = p0 =   in hbar Wave Functions Probability Densities Probability Density

#### Description

The animation shows the time development of a free particle (Gaussian wave packet).  You may change the parameters:  x0, (Dx)2, and p0, then click a link and run the animation.  The graph shows the real (red) and imaginary (green) parts of the wave function, the real (red) and imaginary (green) contributions to the probability density, and the total probability density.  You may right click in the At x = 10 and x = -10 the particle experiences the hard walls of the simulation, otherwise it is free.

#### Questions

Watch each animation for 1.5 time units before changing values and answering the following questions.

1. How does the maximum amplitude and width of the wave packet change with time as you vary x0?
2. How does the maximum amplitude and width of the wave packet change with time as you vary (Dx)2?
3. How does the maximum amplitude and width of the wave packet change with time as you vary p0?
4. Explain why this is.  Try to be as complete as possible.

#### Credits

Script by Mario Belloni and Wolfgang Christian.
Questions by Mario Belloni.
Java applets by Wolfgang Christian.