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98 For electrons in a perfect crystal
101 \begin_layout Theorem
102 there is a basis of wave functions with the following two properties:
105 \begin_layout Standard
106 \begin_inset Separator plain
112 \begin_layout Theorem
113 1) each of these wave functions is an energy eigenstate;
116 \begin_layout Theorem
117 2) each of these wave functions is a Bloch state,
118 meaning that this wave function
119 \begin_inset Formula $\psi$
122 can be written in the form
123 \begin_inset Formula $\psi(r)=u(\boldsymbol{r})e^{i\boldsymbol{k}\cdot\boldsymbol{r}}$
127 \begin_inset Formula $u$
130 has the same periodicity as the atomic structure of the crystal:
132 \begin_inset Formula $u_{\boldsymbol{k}}(\boldsymbol{r})=u_{\boldsymbol{k}}(\boldsymbol{r}+\boldsymbol{n}\cdot\boldsymbol{a})$