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2D Density of States Energy Independentby KingBigness
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#1
Jul1614, 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? 


#2
Jul2014, 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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