Schroedinger's equation

On the following pages, Schrödinger's wave equation is illustrated by a Java-applet.
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The applet
  • original author:  John L. Richardson 
  • further development: Michael Klein
  • Methods for computing the equation numerically:

  • John L. Richardson 
    Visualizing quantum scattering on the CM-2 supercomputer 
    Computer physics communications 63 (1991), S.84-94 
  • The FFT-algorithm is described in: 

  • Babovsky/Beth/Neunzert/Schulz-Reese 
    Math. Methoden in der Systemtheorie: Fourier-Analyse 
    B.G. Teubner, Stuttgart 1987 
Links for more information
University of  Karlsruhe 
Institute of physics at the University of Karlsruhe 
Institute of experimental nuclear physics at the University of  Karlsruhe 
Homepage of Prof. Michael Feindt 
Description of the applet

You see

  • The complex wave function Psi(x,t) with its real part in blue and its imaginary part in green.
  • The residence probability of the particle p(x,t) = | Psi(x,t) | ² as coloured area. The colour represents the phase difference between real and imaginary part (for details click here)
  • The potential V(x) is shown in red.
  • Optionally, a Fourier analysis can be made in every step of computation. The result is shown beneath the wave in black.
You can change: 
  • You can start and stop the computation with the buttons "Start", "Stop", "Pause". While the applet is stopped, the parameters can be modified.
  • In the menu Potential V(x), you can choose one of the prepared potentials.
  • This potential can be modified in height (Höhe) and width (Breite) by using the according text fields.
  • By changing the wave length (Wellenlänge), you kann modify the speed of the wave.
  • The sharpness (Schärfe) of the wave package can also be changed.
Table of contents
Prof. Michael Feindt
Michael Klein

  example #1