including the vacuum energy this time, source of all of humanity's future energy needs. (Right.)
We want to know how Coh(z) evolves (in the Schrödinger picture, since it doesn't evolve in the Heisenberg picture). I.e., we want to compute
Now it would be nice if we could just plug in the formulas we just obtained. Alas, we'd need to compute ea*a eza* (give or take an annoying factor), and the Baker-Campbell-Hausdorff formula we have only helps with eAeB when [A,B] commutes with A and B. Is that the case here?
No such luck, the commutator does not commute with a*a.
Probably we could do something slick anyway, but at least the dull way is quick.
but since e-int = (e-it)n, we can fold this into the (z/sq2)n factor and get:
So after 2 pi seconds, we've got minus the original state vector.