# Quantum Mechanical Scattering...

This JAVA applet integrates the Schrödinger wave equation.
The wave funcition **Psi(x,t)** is initially a guassian wave packet moving to the right.
The wave function, **Psi(x,t)**, is shown
in the shaded region below. The height of the curve is determined by the
probability density
**p(x,t) = |Psi(x,t)|^2 **
and the color is chosen directly from **Psi(x,t)** by a mapping described in
Visualizing Complex Functions.
The **real** and **imaginary** parts of **Psi(x,t)** are shown in **blue** and **green**.
The potential energy function **v(x)** is shown in **red**.

**Notes:**

- The boundary conditions are periodic, so that waves which exit to the right will return on the left.
- The algorithm for integrating the Schrödinger wave equation is from: Richardson, John L.,
*Visualizing quantum scattering on the CM-2 supercomputer*, Computer Physics Communications **63** (1991) pp 84-94

WaveMap.java

John L. Richardson Silicon Graphics, Inc.
E-Mail: jlr@sgi.com http://reality.sgi.com/jlr