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I Density of states from 3D to 2D

  1. Jun 12, 2016 #1
    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
    I should come to 2D conclusion, but I dont see any difference.

  2. jcsd
  3. Jun 12, 2016 #2


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    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.
  4. Jun 12, 2016 #3
    You could try making it very big instead.
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