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Energy distribution function

  1. May 16, 2008 #1
    Hi guys,

    I have a problem understanding the derivation of the energy distribution function; i.e. the number of particles dN with energy dE,

    here is what I have (from literature);

    dN/dE = dN/dt * dt/dV * dV/dE

    so you can define some of these whole derivitives in terms of acceleration (dV/dT), the number of particles you count per unit time (dN/dT) and how velocity varies with energy dV/dE,

    So after plugging in the known quantitites, you end up with something like

    dN/dE = dN/dt * -t^3 / md^2

    where,

    t = time
    N = number of particles
    m = mass
    d = distance

    Now here's my problem, I know that breaking up the dN/dE term into seperate differentiable components make it easier to solve in terms of know quantities ( m,t,d etc.) but what I don't understand is how you get from dN/dE to dN/dt * dt/dV * dV/dE, so in other words, what's the formal procedure for seperating out the derivitaves.

    Hopefuly this is straightforward enough (for you),

    Thanks
    G
     
  2. jcsd
  3. May 16, 2008 #2

    marcusl

    User Avatar
    Science Advisor
    Gold Member

    It's called the Chain Rule of calculus. Just google chain rule and you'll see a hundred explanations and tutorials.

    Here are two:

    http://mathworld.wolfram.com/ChainRule.html" [Broken]

    http://www.math.hmc.edu/calculus/tutorials/chainrule/" [Broken]

    Better is to look in any college calculus text (like those by Thomas).
     
    Last edited by a moderator: May 3, 2017
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