Homework Help: Calculate phase-space volume for 2 kinds of non-interacting particles

1. Oct 20, 2013

dipole

I'm trying to calculate the momentum-contribution of the phase-space volume for a Hamiltonian given by,

$$H = \sum_i^{N_1} \frac{p_i^2}{2m_1} + \sum_j^{N_2} \frac{p_j^2}{2m_2} = E$$

where $m_1$ is the mass of the type-1 particles, and $m_2$ is the mass of the type-2 particles.

This essentially is equivalent to calculating the surface area of an $N = N_1 + N_2$ dimensional ellipsoid, since the momentum coordinates are all constrained to lie on the surface of constant energy $E$.

I'm stuck on how to actually do this though... can anyone help me out or show me how to do so?

Thanks!

Last edited: Oct 20, 2013