WMD - Write my dissertation

bump for interest

>If there's any NMR peeps, I'm sure I can learn a lot from you since you've been looking at photon echos for decades now.

Bumping for NMR or photon echo/nonecho explanations.

Will post a quick summary of my density matrix understanding later today for anyone that may be interested.

Forgot my tripfagging

So, here's the promised summary. If anything is wrong, please point it out.

The density matrix is a way to summarizes a /whole system/ while the wavefunction formalism only allows one state to be described at a time. Of course, one could make the wavefunction more complex and add in more and more details, but it will still only describe a single possible quantum state, while the density matrix allows one to look at all quantum states at once. This is expressed by the sum
[math] \sum_i p_{ij} | \Psi_i \rangle \langle \Psi_j | [/math]
Now for the diagonalization. An eigenbasis can always be chose, but may not be the most convenient basis to work with (at least for me as an experimentalist) so we choose an eigenbasis which we can handle well, namely the energy eigenstates of the atom/molecule/whateversystem we have. Then the diagonal elements of the density matrix can be interpreted as the number of electrons/excitations in that state.
The off-diagonal entries then are the coherence between the populations.
On this I'd still like some more input by you guys as to why this is the correct interpretation, my current understanding is that [math] | \Psi_i \rangle \langle \Psi_j | [/math] acts as a projection of state j onto state i, practically measuring how much of j is in the state i, which can only be non-zero if j and i are coherent.