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140 lines
2.8 KiB
Plaintext
140 lines
2.8 KiB
Plaintext
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#LyX 2.4 created this file. For more info see https://www.lyx.org/
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\lyxformat 614
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\begin_document
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\begin_header
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\save_transient_properties true
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\origin unavailable
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\begin_modules
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theorems-std
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\end_modules
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\maintain_unincluded_children no
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\language italian
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\shortcut idx
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\end_index
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\end_header
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\begin_body
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\begin_layout Title
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Test
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\end_layout
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\begin_layout Theorem
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For electrons in a perfect crystal
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\end_layout
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\begin_layout Theorem
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there is a basis of wave functions with the following two properties:
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\end_layout
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\begin_layout Standard
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\begin_inset Separator plain
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\end_inset
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\end_layout
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\begin_layout Theorem
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1) each of these wave functions is an energy eigenstate;
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\end_layout
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\begin_layout Theorem
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2) each of these wave functions is a Bloch state,
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meaning that this wave function
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\begin_inset Formula $\psi$
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\end_inset
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can be written in the form
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\begin_inset Formula $\psi(r)=u(\boldsymbol{r})e^{i\boldsymbol{k}\cdot\boldsymbol{r}}$
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\end_inset
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where
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\begin_inset Formula $u$
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\end_inset
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has the same periodicity as the atomic structure of the crystal:
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\begin_inset Formula $u_{\boldsymbol{k}}(\boldsymbol{r})=u_{\boldsymbol{k}}(\boldsymbol{r}+\boldsymbol{n}\cdot\boldsymbol{a})$
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\end_inset
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.
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\end_layout
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\end_body
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\end_document
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