Hydrogen formerly Re: "fastfib" in the gf package faster than "fib"

Thanks for the feedback.  I have a general physics question that I hope someone can answer.  I hope it is not too far off topic.

Do you think it would be better to use numerical techniques to do this even for Hydrogen?  I was thinking that I could create an array of maybe dimension 200^3 and store the initial probability distribution state in there and then just use numerical techniques to compute the next state for some small delta of time.  If I were to do this it would probably, I think, be better in the long run anyway since I imagine this is what you have to do most of the time in quantum mechanics anyway.

Also is this something that would be better done in an different language than Lisp or Maxima for speed reasons?  Sorry if I am a little of topic, but I am looking for ways to do this and it may not be that far off topic since applications are one of the uses of Maxima.

Thanks anyone for any ideas.

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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