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Wave packet description of electrons in solid state physics

  1. May 21, 2015 #1
    In solid state physics, I learned that the velocity of a bloch electron is ##\frac{\partial E(k)}{\partial k}##, where ##E(k)## is the energy dispersion. This formula is derived on the basis of the assumption that electrons is a wave packet of bloch state in solids.

    However, I have a question concerning this statement:

    I learned solid state physics three years ago and I am now a Ph.D. student. However, I still cannot convince me of the original statement because I know a wave packet BREAKS DOWN with time evolution. I can't imagine this formula can describe long time evolution of electron states.

    Can anyone give me some confidence of this formula?
  2. jcsd
  3. May 21, 2015 #2


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    This is the velocity for a very broad wavepacket (in real space), i.e. a very localized state in k-space. (If not, for which k-state would you have to take the derivative?) But an infinitely broad wavepacket can't disperse any further.
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