1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Oct 20, 2013 #1
    I'm trying to calculate the momentum-contribution of the phase-space volume for a Hamiltonian given by,

    [tex] H = \sum_i^{N_1} \frac{p_i^2}{2m_1} + \sum_j^{N_2} \frac{p_j^2}{2m_2} = E [/tex]

    where [itex] m_1 [/itex] is the mass of the type-1 particles, and [itex] m_2 [/itex] is the mass of the type-2 particles.

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

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

    Last edited: Oct 20, 2013
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted