# I Density of states from 3D to 2D

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1. Jun 12, 2016

### 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 dont see any difference.

Thanks

2. Jun 12, 2016

### Staff: Mentor

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.

3. Jun 12, 2016

### Jilang

You could try making it very big instead.