Problem 11.7. An approximate expression for the Boltzmann collision operator, , is

where ) are the five orthonormal eigenfunctions of with eigenvalue equal to zero. The five eigenfunctions are 1) = 11), 2) =Px), 3) = Py), |04) = Pz), and los) (3p2/2m)). They are orthonormal with respect to the scalar product,

where n is the number density of particles in the gas described by and m is the mass of the particles.

(b) What are the units of y? What are the units of n?