Quantum Mechanical Scattering
This JAVATM applet integrates the Schrödinger wave equation.
The wave funcition Psi(x,t) is initially a gaussian wave packet moving to the right.
The probability density p(x,t) = |Psi(x,t)|^2 is shown in black.
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. This means that this simulation represents what happens on an infinite line only as long as the left- and right-travelling waves do not "meet" each other.
- The V=0 case represents the dispersion of a gaussian wavepacket on an infinite line, as long as the left and right tails of the wavepacket do not "touch" each other. Note how the phase velocity is only one half of the group velocity, the speed with which the wavepacket moves to the left!
- If this applet runs too slow on your workstation, before buying a faster computer, you might try the smaller version.
- 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
Obviously, this applet requires a Java 1.1 capable browser, with java AND javascript turned on.
| created: 10 Oct 2001 | last modified: 8 Jan 2026 by Nicola Manini |