It's known that the Density of States in 2D is given by,(adsbygoogle = window.adsbygoogle || []).push({});

[tex] g_2(E)dE = \frac{a^2m}{\pi\hbar^2}dE[/tex]

The density of states in 1D and 3D are as follows,

[tex] g_1(E)dE = \left(\frac{a}{\pi}\sqrt{\frac{2m}{\hbar^2}}\right)\frac{1}{\sqrt{E}}dE[/tex]

[tex] g_3(E)dE = \frac{a^3}{2\pi^2}\left(\frac{2m}{\hbar^2}\right)^{\frac{3}{2}}\sqrt{E}dE[/tex]

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?

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# 2D Density of States Energy Independent

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