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With a plane wave, I always took the direction of the wavevector, k, as the direction...

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Physics

With a plane wave, I always took the direction of thewavevector, k, as the direction of propogation (magnitudeproportional to the inverse wavelength). Alternatively, it couldrepresent the momentum (minus a factor ?) of a particle.

However inside a crystal, the electron wavevector and theelectron velocity are not necessarily in the same direction. I'mthinking here of a 2D material with a cylindrical Fermi surfacewhere the momentum may have a z component, but the Fermi velocitydoes not. In everyday cases you would expect momentum and velocityto be in the same direction, moreover I considered the propogationof the wave to be in the same direction as its particleanalogue.

I realise that inside a crystal the electrons are no longersimple plane waves, but what then does the k vector mean?

Answer & Explanation Solved by verified expert
3.6 Ratings (472 Votes)
k points in the direction of phase velocity ie normal to thesurfaces of constant phase also called wavefronts The electronmoves in the direction of group velocity ie a localizedelectron would be made of a    See Answer
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