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How can i solve this multiple Integral?

  1. Feb 15, 2016 #1
    For a bidimensional system of N particles, the hamiltonian of pair-interaction is:
    [tex]H(\vec{q}_1,\vec{q}_2;\vec{p}_1,\vec{p}_2)=K(\vec{p}_1,\vec{p}_2)+U(\vec{q}_1,\vec{q}_2;\vec{p}_1,\vec{p}_2)[/tex]
    where K is the kinetic (translational) energy and U is the potential energy
    i want to solve this multiple integral:
    [tex]\int\int\int\int{e^{-\frac{H(\vec{q}_1,\vec{q}_2;\vec{p}_1,\vec{p}_2)}{{k_BT}}}}d\vec{q}_1d\vec{q}_2d\vec{p}_1d\vec{p}_2[/tex]
    But the pair-potential depends on positions, and momentums as well:
    [tex]U=\frac{k}{\tau}e^{\tau/\tau_0}[/tex]
    where τ0 and κ are parameters and [tex]τ=τ(\vec{q}_{12};\vec{p}_{12})[/tex]
    is a function that depends on relative positions and relative momentums.
    how could i solve this horrible integral? i don't need an analytical solution, a numerical solution with any software like SAGE or Mathematica is fine.
     
  2. jcsd
  3. Feb 16, 2016 #2

    jedishrfu

    Staff: Mentor

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