According to the Bloch's theorem, in periodic potential the wavefunction can be represented as $\Psi_{nk} = u_{nk}(r)e^{ikr}$, where $k$ and $r$ are vectors (I didn't find how to make them bold in equation, sorry) and $u_{nk}$ is a periodic function with the period of lattice constant.
I'm trying to estimate how much $u_{nk}$ depends on $k$. In my problem I have a quantity $u_{n(k+\Delta k)} – u_{nk}$, and I want to know what is my error if I neglect this term. Anselm said in his "Semiconductor theory", Appendix 21, that $u_{nk}$ depends on $k$ weakly and he neglects similar difference. Still, he didn't provide any proof, he only said "it can be shown".
Any ideas where I can find such a proof?
Best Answer
You will find it in
Sandip Tiwari - Semiconductor Physics Principles, Theory and Nanoscale, Oxford University Press, 2020
under chapter 4.6 p 153.