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Hamiltonian describing energy transfer to bloch Electron from EM field

  1. Nov 11, 2011 #1
    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

    \mathscr{H} = \frac{e}{mc}\left[\mathbf{p}(-\mathbf{k}) \cdot
    \mathbf{A}(\mathbf{k}, \omega)\right]

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

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


    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?
  2. jcsd
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