How to derivate Maxwell Boltzmann Distribution

Troller

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)

Jorriss

There are many ways to derive it - some more insightful than others.

Have you taken/taking stat mech?

Troller

Thanks for the answer.
I haven't taken Statistical Mechanics but Statistics. Could it be useful for this?

jtbell

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.

Troller

Thanks. Yeap, here.

1st http://www.eecis.udel.edu/~breech/ph...es/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/Physic...Boltzmann.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.