Hamiltonian describing energy transfer to bloch Electron from EM field

[dkin]

Hi all,

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

$$\begin{equation}<br /> \mathscr{H} = \frac{e}{mc}\left[\mathbf{p}(-\mathbf{k}) \cdot<br /> \mathbf{A}(\mathbf{k}, \omega)\right]<br /> \end{equation}$$

$\mathbf{A}(\mathbf{k}, \omega)$ is the amplitude of the Fourier component of the vector potential for the incident photons with wavevector $\mathbf{k}$ and frequency $\omega$.

$\mathbf{p}(-\mathbf{k})$ is the many particle momentum operator for the electrons with wavevector $-\mathbf{k}$

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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 -k only couple with photons of wave vector k?? If so why?

 

[azntoon]

3) Is the vector potential responsible for coupling the electrons and photons together or is it just a measure of the amplitude of the incident photons?Thanks in advance.