Density of states

  1. Can someone explain to me why the density of states in 2D and 1D includes a step function? I have calculated the DOS in 2D to be:

    [tex]
    D_2(E) = \frac{m_e}{\pi \hbar^2}
    [/tex]

    but in my book there a sum over step functions included so that the expression is:

    [tex]
    D_2(E) = \frac{m_e}{\pi \hbar^2} \sum_m \theta(E - E_m).
    [/tex]

    What does that step function do? It has something to do with the fact that there are a number of quantized states too right?

    Thanks
     
  2. jcsd
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