Density Of States

#Physics

$\displaystyle N=\int , \mathrm{d}N=\int \frac{\mathrm{d}N}{dx} , \mathrm{d}x=\int D(x) , \mathrm{d}x$

• $\displaystyle D(x)$ is the density of states and can be in terms of energy, frequency, or wavenumber

$\displaystyle D(\varepsilon)=\frac{ \mathrm{d}N }{ \mathrm{d}\varepsilon }=\frac{\pi}{2}\left( \frac{2m}{\hbar ^{2}}\left( \frac{L}{\pi} \right)^{2} \right)^{\frac{3}{2}}\varepsilon^{\frac{1}{2}}$

• Density of states for non-relativistic fermions in 3D