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Movies of Quantum Mechanical Phenomena
©1997 by Bernd Thaller

  Here you can download several movies showing quantum mechanical wave functions. The movies are available as QuickTime or MPEG.
Note: The QuickTime movies use the Animation compressor with best quality and are therefore much larger than the corresponding mpeg movies.
Do you know that the QuickTime Plug-in lets you view QuickTime movies directly in the browser window of Netscape Navigator 3.0? Download the QuickTime-plugin (MacOS, Windows 3.1, Windows 95)
  Wave functions are complex-valued functions. The absolute value containes information on the localization of the particle, the phase gives additional information about the dynamical state. We use a color code to visualize complex numbers. This color mapping of the complex plane is described in the illustration to the right. It is a stereographic projection of the surface of the three dimensional color manifold onto the compactified complex plane.
  color map (JPEG, 30k)

  Movies showing solutions of the Schrödinger equation in one dimension:  
Repulsive Square Well Potential
QuickTime (755K), MPEG (435K)

Movie showing the one-dimensional motion of a gaussian wave packet hitting a repulsive square well potential. The size of the potential is equal to the average kinetic energy of the particle.

Reflectionless Potential
QuickTime (1500K), MPEG (747K)

Gaussian wave packet meets a reflectionless potential (soliton of the Korteweg deVries equation in one dimension).
Resonance Scattering
QuickTime (952K), MPEG (551K)

Resonant scattering state in one dimension. The particle remains in the interaction region much longer than can be expected from classical considerations. Both at higher and at lower energies only a much smaller amount of the wavepacket can enter the region between the wall and the obstacle.
Harmonic Oscillator in 1D
QuickTime (1340K), MPEG (774K)

Squeezed state of a harmonic oscillator. The initial state is a Gaussian wave packet. The behaviour is quite similar to the classical motion.
  Solutions of the Schrödinger equation in two dimensions:  
Double Slit
QuickTime (2755K), MPEG (842K)

The movie shows the famous double-slit experiment with a Gaussian initial state.
Attractive Gaussian Potential
QuickTime (2828K), MPEG (737K)

Particle being scattered at the potential -Exp[-x^2] (smooth, attractive potential well) in two dimensions. The particle hits the interaction region with a nonzero impact parameter.

  The movies were generated with the help of Mathematica. Numerical calculations were performed with the InterCall package.

All this is part of a larger project:
The final goal is a "movie book of quantum mechanics", a book/CD combination with an introductory text on quantum mechanics and a huge collection of animated illustrations presented in trendy multimedia style. Please, write me an e-mail, if you have suggestions or comments!

Here you can download the Mathematica packages used for the visualizations in one and two dimensions. These are in a sort of beta state and far from being perfect or highly optimized:


  Here you can see some examples of visualizations generated with the software package AVS ("Application Visualization System" by Advanced Visual Systems Inc.). These visualizations were made in collaboration with Jutta Pauschenwein.

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Bernd Thaller
Institute of Mathematics
University of Graz

Mail to: Bernd Thaller, last change:07-03-1997