Commit 0c24a5d8 authored by Anton Akhmerov's avatar Anton Akhmerov
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typo fix; closes #30

parent 79eaa4cc
......@@ -27,7 +27,7 @@ $$
\mathcal{H}=\frac{ {\bf p}^2}{2m}=-\frac{\hbar^2}{2m}\left( \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2} \right)\ \Rightarrow\ \varepsilon=\frac{\hbar^2}{2m}\left( k_x^2+k_y^2+k_z^2 \right)
$$
If we impose periodic boundary conditions, $\psi(x,y,z)=\psi(x+l,y+L,z+L)$, it follows that the allowed wavenumbers are given by
If we impose periodic boundary conditions, $\psi(x,y,z)=\psi(x+L,y+L,z+L)$, it follows that the allowed wavenumbers are given by
$$
k_x=\frac{2\pi p}{L},\ k_y=\frac{2\pi q}{L},\ k_z=\frac{2\pi r}{L}\ \Rightarrow\ \varepsilon=\frac{2\pi^2\hbar^2}{mL^2}\left( p^2+q^2+r^2 \right).
......
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