# Integral of Maxwell-Boltzmann

1. Jul 7, 2010

### Monty Hall

I'm reading http://www.ndsu.edu/fileadmin/physics.ndsu.edu/Wagner/LBbook.pdf (pg 12, 3.2.2) about the lattice boltzmann method. I'm speaking of his specfic form of the Maxwell-Boltzman and his claim that the integral of equilibrium distribution is equal to n

$$\int f^0 = n$$

$$f^0(v)=\frac{n}{(2\pi\theta)^{3/2}}e^{-(v-u)^2/2\theta}$$

But when I use gaussian integrals I don't get n but rather $$\frac{n}{2\pi\theta}$$. What am I missing?

2. Jul 7, 2010

### zhermes

From a quick glance, your answer seems correct; if the integral was to be just n, then the leading denominator would have to be

$$\sqrt{2 \pi \theta}$$

3. Jul 7, 2010

### Monty Hall

Thanks for your reply. When I look at the wikipedia version of the maxwell-boltzman, I see they do a triple integral over basically the same equation, there I get N. From how the author wrote the equation, there was no indication that he was speaking of velocity and not speed like bold face or overarrows. Plus it doesn't help that I'm not familiar with statistical mechanics either).

4. Jul 7, 2010

### zhermes

That makes sense; poor form that they didn't make that more clear--either they should have had all 3 serifs, or vectors over their velocities or something.