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Black holes, white dwarfs and neutron stars-Shapiro, Teukolsky

  1. Nov 18, 2014 #1
    1. The problem statement, all variables and given/known data
    Hello, I try to recompute all exercises in this book and sometime I hit the snag :) One of the first is:
    Exercise 2.6 (page 28)
    Show that mean kinetic energy of an electron in a degenerate gas is [itex]\frac{3}{5}E'_f [/itex] in the nonrelativistic limit and [itex]\frac{4}{5}E_f [/itex] in relativistic limit. Here [itex]E'_f=E_f-m_ec^2=p_f^2/2m_e [/itex].

    2. Relevant equations


    3. The attempt at a solution
    I know that for nonrelativistic limit [itex]\epsilon=\frac{m_ec^2}{\lambda_e^3 \pi^2}\chi(x)[/itex] and [itex]\chi(x)->\frac{x^3}{3\pi^2} [/itex]. So my idea was to integrate this energy density from 0 to x-fermi, where [itex]x=p/mc[/itex]. But result [itex]\frac{2\pi}{3h^3}cp_f^4[/itex] doesnt recover their.
    Do have anybody some suggestions?
     
  2. jcsd
  3. Nov 23, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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