# 2D Density of States Energy Independent

by KingBigness
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 P: 96 It's known that the Density of States in 2D is given by, $$g_2(E)dE = \frac{a^2m}{\pi\hbar^2}dE$$ The density of states in 1D and 3D are as follows, $$g_1(E)dE = \left(\frac{a}{\pi}\sqrt{\frac{2m}{\hbar^2}}\right)\frac{1}{\sqrt{E}}dE$$ $$g_3(E)dE = \frac{a^3}{2\pi^2}\left(\frac{2m}{\hbar^2}\right)^{\frac{3}{2}}\sqrt{E} dE$$ It's clear that the 1D and 3D Density of States are dependent on energy but it seems for the 2D case the energy density is constant. I was wondering why this was the case?