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classical_density_of_states [2016/03/09 12:48] nikolaj |
classical_density_of_states [2016/03/09 12:49] nikolaj |
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| ^ $ D(E) = 2\pi\ 2\frac{V}{(2\pi)^3}(\hbar c)^{-3}\cdot E^2 $ ^ | ^ $ D(E) = 2\pi\ 2\frac{V}{(2\pi)^3}(\hbar c)^{-3}\cdot E^2 $ ^ | ||
| - | More generally, for an dispersion relation $E=E_0+a\,k^p$ in an $n$-dimensional space (volume of the space being $b\,k^n$), the density is | + | More generally, for an dispersion relation $E=E_0+c_k\,k^p$ in an $n$-dimensional space (volume of the space being $c_n\,k^n$), the density is |
| $D(E) = \dfrac{c_n}{c_k^r}\dfrac{\mathrm d}{{\mathrm d}E}(E-E_0)^r=r\,\dfrac{c_n}{c_k^r}(E-E_0)^{r-1}$, where $r:=\tfrac{n}{p}$. | $D(E) = \dfrac{c_n}{c_k^r}\dfrac{\mathrm d}{{\mathrm d}E}(E-E_0)^r=r\,\dfrac{c_n}{c_k^r}(E-E_0)^{r-1}$, where $r:=\tfrac{n}{p}$. | ||
