Since the actual magnetic field would change at some finite (though fast) rate, I cannot use the projection of the initial state on the states at the end. That means I cannot assume the instantaneous aprroximation for the entire 2T range. I can only assume the instantaneous approximation for...
well like I said, I can do this task manually for a specific crossing. I decide "by sight" where the crossings begins and where it ends, and I take the dot product of the initial eigenstate (just before the crossings) with eigenstates just after the crossing. The "end eigenstate" should be the...
I still haven't verified it, but it should be due to the states ceasing to have a clear up or down character for each ion. Instead ions should have an up+-down character at these high fields
I'm interested in the sudden approximation as I've said.
The problem is that here I have multiple levels interacting and the width of the avoided crossings varies considerably. If I just had two levels, I could study them in detail and compare the eigenstates before the crossings to those...
Thanks DrDu, I am indeed interested in the sudden approximation.
If I understand you correctly than I've already tried this.
Perhaps the graphic results would illustrate my problem better.
The figure shows the energy levels as a function of applied field. let's say I start at the top...
I have diagonalized a Hamiltonian matrix many times with a varying parameter (varying magnetic field).
This gives me the eigenstates and eigenvalues of the matrix for the different field values.
I now need to track the diabatic states through (avoided) level crossings of the eigenvalues...