1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statistical mechanics question - please help

  1. May 12, 2010 #1
    We're covering probability of the distance for free electrons with parallel spin (long-range oscillations should go to zero) and using that to get a correlation energy. My teacher wants us to elaborate the following 1D case.

    [tex]


    \int e^{ik(x-X)}dk=\frac{e^{ik(x-X)}}{i(x-X)}\Rightarrow Re\left (\frac{e^{ik(x-X)}}{i(x-X)} \right ) =\frac{sin[k(x-X)]}{x-X}


    [/tex]

    Taking X = 0 and evaluating for case 1 from 0 to k_0 and for case 2 from 0 to 2k_0 (where k_0 is at the Fermi level) my teacher wrote:

    [tex]

    \psi_{1} \sim \frac{sin(k_{0}x)}{k_{0}x}

    [/tex]

    [tex]

    \psi_{2} \sim \frac{sin(2k_{0}x)}{2k_{0}x}

    [/tex]

    I think to get the k_0 in the denominator for the first one and 2k_0 in the denominator for the second one he multiplied both sides by k_0/k_0 and 2k_0/2k_0, respectively.

    Here is my question:

    My teacher says the first one is supposed to be the filled state, the second one the empty state - why? A lot of this, conceptually, is very unclear to me.
     
    Last edited: May 13, 2010
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Statistical mechanics question - please help
  1. Statistical Mechanics (Replies: 0)

  2. Statistical mechanics (Replies: 0)

Loading...