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2D Density of States Energy Independent

by KingBigness
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Jul16-14, 12:36 AM
P: 96
It's known that the Density of States in 2D is given by,
[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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Jul20-14, 10:29 AM
P: 100
this is for a free electron. Not necessarily for every system.

I don't have a physical intuitive explanation. It just arises from the math of the system.

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