"fastfib" in the gf package faster than "fib"

Computing the eigenvalues may not be a problem.  The problem is displaying the result.  To get really nice output I would divide the cube by 200 by 200 by 200 giving 200^3 points, then I would have to compute the probability density for each point, 200^3 of them.  The I have to have about 200 frames for a short clip.  So make that 200^4. The there is the graphics calculations.  Anyway I have already decided I am not going to do it.  It's just not worth it.

Rich 




 ------------Original Message------------
From: Michel Talon <talon at lpthe.jussieu.fr>
To: maxima at math.utexas.edu
Date: Thu, Jul-10-2008 4:18 AM
Subject: Re: [Maxima] "fastfib" in the gf package faster than "fib"

Richard Hennessy wrote:

> In other words I want to watch the hydrogen atoms electron cloud change
> shape, so the output would be a movie clip maybe using
> draw(terminal=animated_gif, etc...
> 
> 

I don't think these specific computations are so terrible. Projecting a
given initial state on the known hydrogen atom eigenfunctions is just a
matter of computing some integrals, numerically. In fact such an integral
is an integral on r, theta and phi, and the integrals on theta and phi
are quite simple numerically. I assume Gauss integration will do fine.
The integral on r may be more troublesome since it runs from 0 to infinity,
and i suppose that if the initial state is localized close to the origin 
only the first quantum numbers n will produce significant result, and the
integral will cut out to small values of r.
Once this done each state evolves in time trivially by exp(-iEt/hbar) and
one just needs to sum back the few states involved, and compute the square
to get the probability. The problem which is complex is the atom or
molecule with a lot of electrons, but even that problem is routinely
treated by theoretical chemists. Here of course one needs sophisticated
techniques from numerical analysis.


-- 
Michel Talon
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