Here's a simulation of a wave-packet in two dimensions scattered from a
potential resembling a wall with a slit, very much like the famous
diffraction-experiments seen with electron beams. This is kind of a test
rendering; initial conditions are like kind of arbitrary. I am working on a
visualization project at the University of Oslo, and this is some of the
work I am doing there.

I used the Leapfrog-Algorithm in C++ to simuate the wave-function on a
200x200-grid of doubles. The output is hundreds of PPM-files used as
height-fields.

Comments are welcome! What can be done to perhaps make it even more
illustrating? As for now, I am quite happy with the texture of the wave, but
as I said, comments/suggestions are welcome! :)

URL: http://www.fys.uio.no/~simenkva/animations/diffr.mpg


regards,
Simen Kvaal.

--
---------------------------------------------
Simen Kvaal, Student at the faculty of
mathematics and natural sciences, University
of Oslo, Norway.
e-mail: sim### [at] studentmatnatuiono
web: http://www.uio.no/~simenkv/
---------------------------------------------

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in news:3b6d28f6$1@news.povray.org Simen Kvaal wrote:

> Comments are welcome! What can be done to perhaps make it even more
> illustrating? As for now, I am quite happy with the texture of the
> wave, but as I said, comments/suggestions are welcome! :)

Fascinating.
If the hight of the wave has any importance in the experiment, maybe 
add a slight gradient. Maybe make the green walls of he slit (semi) 
transparent.

Ingo

-- 
Photography: http://members.home.nl/ingoogni/
Pov-Ray    : http://members.home.nl/seed7/

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In article <3b6d28f6$1@news.povray.org>, Simen Kvaal says...
> Here's a simulation of a wave-packet in two dimensions scattered from a
> potential resembling a wall with a slit, very much like the famous
> diffraction-experiments seen with electron beams. This is kind of a test
> rendering; initial conditions are like kind of arbitrary. I am working on a
> visualization project at the University of Oslo, and this is some of the
> work I am doing there.
> 
> I used the Leapfrog-Algorithm in C++ to simuate the wave-function on a
> 200x200-grid of doubles. The output is hundreds of PPM-files used as
> height-fields.
> 
> Comments are welcome! What can be done to perhaps make it even more
> illustrating? As for now, I am quite happy with the texture of the wave, but
> as I said, comments/suggestions are welcome! :)
> 
What happens after the reflection that makes the energy seem to break up 
in small parts the size of the grid squares?

On the whole it is great: makes the quantum theory a little 'visible' to 
the layman. :)
-- 
Regards,  Sander

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Sander wrote:
> What happens after the reflection that makes the energy seem to break up
> in small parts the size of the grid squares?
> 

It stems from interference, and the match with the grid might be
caused by that the speed of the wave happens to be an integer. (The
grid lines have integer spacing; 2.)

Also remember that the wave equation is slightly different from the
usual "surface" or "water" equation, so the behaviour is not the same.

Simen.

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ingo wrote:
> 
> Fascinating.
> If the hight of the wave has any importance in the experiment, maybe
> add a slight gradient. Maybe make the green walls of he slit (semi)
> transparent.
> 

Thanks for the suggestions!

I've tried several things with the barrier, but I find it a bit
confusing. A slight gradient is a possibility; I'll try some
variations and maybe post some stills if it turns out better.


Simen.

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Simon -

I'm a Ph.D. student in Physics at the University of Nebraska.  I'm
always looking for cool visualizations of quantum mechanics, and I'm
pretty impressed by this animation! 

I've experimented with using color coding to denote the phase of the
wavefunction, and it seems to work pretty well.  Is that something you'd
be interested in doing?

Also, the thing that interests me the most right now is visualizing the
time dependent scattering of a photon pulse on an atom or something like
that... but who has the time?

- Ben

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It wouldn't make it any more viewabel, but it would make it pretty - why
not try a water/glass transparent texture for the heightfield ?

Simen Kvaal wrote:
> 
> Here's a simulation of a wave-packet in two dimensions scattered from a
> potential resembling a wall with a slit, very much like the famous
> diffraction-experiments seen with electron beams. This is kind of a test
> rendering; initial conditions are like kind of arbitrary. I am working on a
> visualization project at the University of Oslo, and this is some of the
> work I am doing there.
> 
> I used the Leapfrog-Algorithm in C++ to simuate the wave-function on a
> 200x200-grid of doubles. The output is hundreds of PPM-files used as
> height-fields.
> 
> Comments are welcome! What can be done to perhaps make it even more
> illustrating? As for now, I am quite happy with the texture of the wave, but
> as I said, comments/suggestions are welcome! :)
> 
> URL: http://www.fys.uio.no/~simenkva/animations/diffr.mpg
> 
> regards,
> Simen Kvaal.
> 
> --
> ---------------------------------------------
> Simen Kvaal, Student at the faculty of
> mathematics and natural sciences, University
> of Oslo, Norway.
> e-mail: sim### [at] studentmatnatuiono
> web: http://www.uio.no/~simenkv/
> ---------------------------------------------

-- 
Oliver Wood
University Of Durham

http://www.dur.ac.uk/o.e.wood/

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