Density of states from 3D to 2D

[Matej Kurtulik]

Hi,
I know how to calculate density of states for both cases, but it is not clearly to me how I can go from 3D case to 2D. I have energy from infinite potential well for 3D
$$E=\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{l_x}+\frac{n_y^2}{l_y}+\frac{n_z^2}{l_z})$$
let make one dimension very small
$$l_x<<1$$
I should come to 2D conclusion, but I don't see any difference.

Thanks

 

[DrClaude]

If $l_x$ is extremely small, then the only possible value of $n_x$ is 0, as the energy for excitation would be too big. The system is then reduced to 2D.

 

[Jilang]

You could try making it very big instead.