diff --git a/src/2_debye_model_solutions.md b/src/2_debye_model_solutions.md index 61621dfabb2f104e6f0055de1432327cfdb0ad9d..71708ec430ee1962f2c8c2819334e9adee13f0b0 100644 --- a/src/2_debye_model_solutions.md +++ b/src/2_debye_model_solutions.md @@ -78,7 +78,7 @@ For 1D we have that $N = \frac{L}{2\pi}\int_{-k}^{k} dk$, hence $g(\omega) = \fr For 2D we have that $N = 2\left(\frac{L}{2\pi}\right)^2\int d^2k = 2\left(\frac{L}{2\pi}\right)^2\int 2\pi kdk$, hence $g(\omega) = \frac{L^2\omega}{\pi v^2}$. -For 3D we have that $N = 3\left(\frac{L}{2\pi}\right)^3\int d^3k = 3\left(\frac{L}{2\pi}\right)^3\int 4\pi kdk$, hence $g(\omega) = \frac{3L^3\omega^2}{2\pi^2v^3}$. +For 3D we have that $N = 3\left(\frac{L}{2\pi}\right)^3\int d^3k = 3\left(\frac{L}{2\pi}\right)^3\int 4\pi k^2dk$, hence $g(\omega) = \frac{3L^3\omega^2}{2\pi^2v^3}$. ### Exercise 2: Debye model in 2D.