# Tutorials

## Scattering Tutorials

As an aid to understanding quantum mechanical scattering, we have developed a short tutorial, and a series of Java Applets. The tutorial is currently only available as a pdf file:

## Scattering off of a well

Here is a little Java applet for investigating the phase-shifts for s-wave scattering off of a square well. The applet makes use of an engine called LiveGraphics3D .

Move your mouse over the square below, and the applet should load.

On the left is the potential. By dragging the three black points you can change the potential. Approximate energies of the bound states/resonances are given as red lines. The scattering length and "effective range" are respectively given by red and green dots. On the vertical axis, some points are given in units of V0=(2 pi hbar)^2/2m x^2, where x is the width of the well. On the right is the scattering phase shift as a function of kx.

Some points to note: 1) When a bound state is just below threshold, the scattering length is large and positive. 2) When the resonant state is just above threshold, the scattering length is large and negative. 3) The phase shift at k=0 gives the number of bound states. 4) The phase shift vanishes at k=infinity. 5) There is only one dimensionless parameter in the problem (hence the sliding scale for the potential).