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How to derivate Maxwell Boltzmann Distribution

  1. Jan 5, 2013 #1
    Hi PFers. I am interested in Maxwell Boltzmann Distribution. I have searched in Internet for the derivation but I am not satified with them. Can somebody show me the way to derivate it? Thanks.
    ψ(v)=(m/2*pi*kT)^(3/2) e^(-mv^2/2kT)
    Last edited: Jan 5, 2013
  2. jcsd
  3. Jan 5, 2013 #2
    There are many ways to derive it - some more insightful than others.

    Have you taken/taking stat mech?
  4. Jan 5, 2013 #3
    Thanks for the answer.
    I haven't taken Statistical Mechanics but Statistics. Could it be useful for this?
  5. Jan 5, 2013 #4


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    Staff: Mentor

    It would help if you tell us why you are not satisfied. Then people won't waste time pointing you to the same things again. :smile:
  6. Jan 6, 2013 #5
    Thanks. Yeap, here.

    1st http://www.eecis.udel.edu/~breech/physics/physics-notes/node32.html

    Sorry I haven't used LaTeX well enough to type it here again. At derivation of ψ(v)=f(vx)f(vy)f(vz) by taking derivatives with respect to vx, it is very unclear to me. I think dψ/dvx = dψ/dv * dv/dvx. And after that I dont know how to solve it.

    2nd http://www.maxwellsociety.net/PhysicsCorner/Miscellaneous Topics/MaxwellBoltzmann.html

    This seems better and easier. At the part argumenting for spherical shell, there are a lot of values of vx/y/z so that give the same value of v!? And the application of function g(v)=[itex]\alpha[/itex]v^n * e^(-[itex]\beta[/itex]v^2) is a bit evidencelessly.
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