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Solutions lecture 7

Merged Lars kleyn Winkel requested to merge solutions-lecture-7 into master
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@@ -195,7 +195,7 @@ E = E_0 - 2t\cos{ka} \approx E_0 - 2t + t (ka)^2.
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Comparing this with $E=(\hbar k)^2/2m$, we see that the dispersion is similar to that of free electrons but with an effective mass given by $m^*=\hbar^2/2ta^2$.
Notice that in this particular case we can occupy a continuous band from $E_0+t$ to $E_0-t$, in the next lecture we shall see that small deviations in the hopping between two adjacent atoms can change the continuity of the band! The \textit{band structure} of the electrons now consists of two **separate** bands. The complete dispersion relation is also called a *band structure*.
Notice that in this particular case we can occupy a continuous band from $E_0+2t$ to $E_0-2t$, in the next lecture we shall see that small deviations in the hopping between two adjacent atoms can change the continuity of the band! The *band structure* of the electrons now consists of two **separate** bands. The complete dispersion relation is also called a *band structure*.
### Group velocity, effective mass, density of states
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