Subject: "fastfib" in the gf package faster than "fib"
From: Michel Talon
Date: Thu, 10 Jul 2008 10:18:49 +0200
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