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Boltzmann equation

  1. Jun 6, 2010 #1

    I am trying to make the following equation to get Boltzmann equation which I write below.
    f(\mathbf{x}+\frac{\mathbf{p}}{m}dt,\mathbf{p} + \mathbf{F}dt,t+dt) \,d\mathbf{x}\,d\mathbf{p}
    - f(\mathbf{x},\mathbf{p},t)d\mathbf{x}\,d\mathbf{p} =
    \left. \frac{\partial f(\mathbf{x},\mathbf{p},t)}{\partial t} \right|_{\mathrm{coll}} \, d\mathbf{x} \, d\mathbf{p} \, dt

    Boltzmann equation:
    \frac{\partial f}{\partial t}
    + \frac{\partial f}{\partial \mathbf{x}} \cdot \frac{\mathbf{p}}{m}
    + \frac{\partial f}{\partial \mathbf{p}} \cdot \mathbf{F}
    = \left. \frac{\partial f}{\partial t} \right|_{\mathrm{coll}}

    So, should I do partial differentiation? But how to do that since I do not know the function exactly.. Can someone give me some guidances? Many thanks before.
  2. jcsd
  3. Jun 14, 2010 #2

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