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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?

    Thanks!
     
    Last edited: Oct 20, 2013
  2. jcsd
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