Re: Solving TD/TI Schrod eq in 2/3 dimen
- To: mathgroup at smc.vnet.net
- Subject: [mg20590] Re: Solving TD/TI Schrod eq in 2/3 dimen
- From: "Kevin J. McCann" <kevinmccann at Home.com>
- Date: Tue, 2 Nov 1999 02:35:27 -0500
- Organization: @Home Network
- References: <7vfeol$kbk@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
There is no exact solution for H2, but there is for the H2+ ion, although it ain't pretty. I don't have a reference handy, but might be able to dig one out if you need it. The whole field of doing X2 molecules with varying internuclear separation has been around for a long time, but it is a fairly time consuming calculation. The usual approach is to expand in Gaussians or some other analytic function for which all integrals are known analytically. Haven't done this myself, but I have used the results often for scattering calculations. A good place to look would be in the Journal of Chemical Physics. I suspect that Mathematica is NOT the way to go, since this can be a seriously difficult calculation. If you find some nice solution I would really like to hear from you. In answer to your second question. You can actually reduce the dimensionality of the problem by expanding in spherical harmonics with the z-axis along the internuclear line. I don't know where you are on the learning curve about the generalities, but the chemists often have useful references. I especially like this oldy but goody, although I am sure there are more recent references. "Atoms & Molecules" by Martin Karplus and Richard Porter W. A. Benjamin 1971 Kevin Jordan Maclay <jordanmaclay at quantumfields.com> wrote in message news:7vfeol$kbk at smc.vnet.net... > > 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 > www.quantumfields.com > jordanmaclay at quantumfields.com