A Bloch wave has the following form..(adsbygoogle = window.adsbygoogle || []).push({});

## \Psi_{nk}(r)=e^{ik\cdot r}u_{nk}(r)##

The ##u_{nk}## part is said to be periodic in real space. But what about reciprocal space? I've had a hard time finding a direct answer to this question, but I seem to remember reading somewhere that the entire Bloch wave is periodic in k-space i.e. ##\Psi_{nk}(r)=\Psi_{n(k+G)}(r).## In that case, whatever additional exponential factor ##e^{iG\cdot r}## we gained from a k-space translation must occur as ##e^{-iG\cdot r}## in the ##u_{nk}## piece. How can we tell without knowing the exact form of the ##u_{nk}## piece though? I think that ##u_{nk}## comes from the fourier coefficients of the periodic potential. Maybe it has something to do with this?

Thanks.

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# Is a Bloch wave periodic in reciprocal space?

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