Derive unitary operator for circular orbits withn quasiclassical approximation
The most simple thing to calculate is evolution operator for circular trajectories on isotropic disc with approximation that spins do not fluctuate. I have just finished such calculation which gives a useful result.
Over the next weeks, I would like you to deduce such calculation yourself and put the derivation in new notes. The steps of derivation:
- Deduce how to calculate U, with
\sigma_z
andL_z
. That is basically done in your previous notes. - Deduce that contribution from
L_z
is0
. - Calculate overlap between
<\psi_+|\psi_->
and\sigma_z
projection on the valley states.
The calculation of overlap and \sigma_z
will be certainly useful for later stages.