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Solving TD/TI Schrod eq in 2/3 dimen

• To: mathgroup at smc.vnet.net
• Subject: [mg20570] Solving TD/TI Schrod eq in 2/3 dimen
• From: "Jordan Maclay" <jordanmaclay at quantumfields.com>
• Date: Sat, 30 Oct 1999 14:54:50 -0400
• Organization: Quantum Fields LLC
• Sender: owner-wri-mathgroup at wolfram.com

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