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Re: Solving TD/TI Schrod eq in 2/3 dimen

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  • Subject: [mg20590] Re: Solving TD/TI Schrod eq in 2/3 dimen
  • From: "Kevin J. McCann" <kevinmccann at>
  • Date: Tue, 2 Nov 1999 02:35:27 -0500
  • Organization: @Home Network
  • References: <7vfeol$>
  • Sender: owner-wri-mathgroup at

There is no exact solution for H2, but there is for the H2+ ion, although it
ain't pretty.  I don't have a reference handy, but might be able to dig one
out if you need it.  The whole field of doing X2 molecules with varying
internuclear separation has been around for a long time, but it is a fairly
time consuming calculation.  The usual approach is to expand in Gaussians or
some other analytic function for which all integrals are known analytically.
Haven't done this myself, but I have used the results often for scattering
calculations.  A good place to look would be in the Journal of Chemical
Physics.  I suspect that Mathematica is NOT the way to go, since this can be a
seriously difficult calculation.  If you find some nice solution I would
really like to hear from you.

In answer to your second question.  You can actually reduce the
dimensionality of the problem by expanding in spherical harmonics with the
z-axis along the internuclear line.  I don't know where you are on the
learning curve about the generalities, but the chemists often have useful
references.  I especially like this oldy but goody, although I am sure there
are more recent references.

"Atoms & Molecules"
by Martin Karplus and Richard Porter
W. A. Benjamin 1971


Jordan Maclay <jordanmaclay at> wrote in message
news:7vfeol$kbk at
> I am new to the numerical approach here and would greatly welcome some
> practical advice:
> Ideally I want to solve the Schrodinger equation in 3 dimensions with a
> slowly varying time dependent, spatial dependent perturbation (B field),
> for a the hydrogen molecule.  I am interested in how the perturbation
> affects the ground state wavefunction.  To simplify, I want to specify
> the internuclear separation R, and assume the nuclei are fixed.  The
> perturbation is slow enough so the adibatic approximation would be
> valid.  Solutions to the lowest order in adibatic perturbation theory
> would probably be ok.  "Exact" solutions would be great, if practical.
> I don't have any idea if this will take years or days to do in 3D.
> Should I try to reduce the problem to 2 D?  Any suggestions on a
> practical approach would be very appreciated.
> Jordan Maclay
> Chief Scientist
> Quantum Fields LLC
> jordanmaclay at

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