Classical Molecules

xantox, 9 July 2007 in Gallery

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3 Comments to “Classical Molecules”

  1. 1

    This seems to be a classical simulation, but with a “Pauli force” added in somehow. Can you explain what was done here? Presumably a fully quantum simulation could also be done with the charge distributions, which might be interesting to compare.

  2. 2

    The “Pauli” force here is a repulsive force that goes as the inverse of the radial distance r between any two of the charges raised to the power 12. The attractive force between say a positive and negative charge only goes as the inverse of the radial distance between the two charges raised to the power 2. Thus at far distances (far being large compared to the radius of the spheres in the animation) the inverse r squared term dominates and opposite charges will see an attraction and move together, but when they are close enough the inverse r to the 12 term dominates and they are repelled. The inverse r to the 12 term is very “hard”, meaning the transition between attraction and repulsion occurs very rapidly, which is why the charges appear to “bounce” when they collide. The quantum mechanical calculation would show the evolution of the symmetric or anti-symmetric wave functions of the particles, and (1) would be much much much harder to compute and (2) could not be compared directly to the above (I don’t think).

  3. 3
    Ed Sanville

    If you did the quantum calculations, you could start with a quantum state of a gaussian wavepacket for each particle, and plot the single particle density function, (integrate the wavefunction squared over all the coordinates except each particle in the system). Of course, this is assuming that the individual particles are distinguishable, which probably wouldn’t be the case in reality. It would still be interesting to watch though.

    By the way, nice movie!

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