deletions | additions       diff --git a/photoemission2.tex b/photoemission2.tex  index baea2f2..7c58ac0 100644  --- a/photoemission2.tex  +++ b/photoemission2.tex 
...
in $B$.   It is the time-evolution operator associated with the Hamiltonian $\hat{H}_{\rm v}$ describing free electrons in   an oscillating field.   Given a time dependent vector field $\vec{\mathrm{A}}(t)$, $\vec{{A}}(t)$,  the Hamiltonian $\hat{H}_{\rm v}=\frac{1}{2}(-i\vec{\nabla}-\frac{\vec{\mathrm{A}}(t)}{c})^2$ v}=\frac{1}{2}(-i\vec{\nabla}-\frac{\vec{{A}}(t)}{c})^2$  expressed in the velocity gauge is diagonal in momentum and can be naturally applied to $\phi^B_i(\vec{k},t)$.  For all systems that can be described by a Hamiltonian such that $\hat{H}(\vec{r},t)=\hat{H}_{\rm v}(\vec{r},t)$