# How to derivate Maxwell Boltzmann Distribution

1. Jan 5, 2013

### 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)

Last edited: Jan 5, 2013
2. Jan 5, 2013

### Jorriss

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

Have you taken/taking stat mech?

3. Jan 5, 2013

### Troller

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

4. Jan 5, 2013

### 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.

5. Jan 6, 2013

### Troller

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)=$\alpha$v^n * e^(-$\beta$v^2) is a bit evidencelessly.