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When an electron is excited from valence band to conduction band, it has to have a finite momentum in the case of indirect bandgap. Does that mean that the electron cannot be created at rest ? does it have a non zero "speed" ?

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It means that to fulfill momentum conservation law, the momentum should be taken from somewhere: from phonons, impurities, etc.

The speed is a derivative of the energy (remember Hamilton's equations), thus the speed is zero at the minimum of the energy, wherever this point is located in k space

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I am not familiar with Hamilton's formulations. Does that mean that momentum is not equal to mass*speed for electrons in a solid ? –  oliver34 Oct 23 '11 at 8:04
    
In general case $v\equiv\dot{q}=\frac{\partial H}{\partial p}$ which leads to $\dot{q}=p/m$ only if $H=\frac{p^2}{2m}+U(q)$ –  Misha Oct 23 '11 at 9:24
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