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I've a hamiltonian that describes the coupling of electrons in a crystal (bloch electrons) to an EM field described by a vector potentialA

[tex]

\begin{equation}

\mathscr{H} = \frac{e}{mc}\left[\mathbf{p}(-\mathbf{k}) \cdot

\mathbf{A}(\mathbf{k}, \omega)\right]

\end{equation}

[/tex]

[itex]\mathbf{A}(\mathbf{k}, \omega)[/itex] is the amplitude of the fourier component of the vector potential for the incidentphotonswith wavevector [itex]\mathbf{k}[/itex] and frequency [itex]\omega[/itex].

[itex]\mathbf{p}(-\mathbf{k})[/itex] is the many particle momentum operator for theelectronswith wavevector [itex]-\mathbf{k}[/itex]

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Here are my questions if anyone would be so kind as to help.

1) How does this equation result in an energy value??

2) Can electrons with wave vector-konly couple with photons of wave vectork?? If so why?

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# Hamiltonian describing energy transfer to bloch Electron from EM field

Can you offer guidance or do you also need help?

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