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Distributive of the classical Liouville operator

  1. Oct 22, 2009 #1
    I'm trying to derive fokker-planck equations using the Liouville operator for classical systems. part of it relies on a property i've seen in many places, that applying the Liouville operator [tex]e^{Lt}[/tex] to a product of two functions [tex]A(\textbf{X})B(\textbf{X})[/tex] is the same as applying the Liouville operator to both of them individually, i.e.:

    [tex] e^{Lt}(A(\textbf{X})\cdot B(\textbf{X})) = (e^{Lt}A(\textbf{X}))\cdot (e^{Lt}B(\textbf{X}))[/tex]

    this seems to make sense physically but does anyone know a proof? it seems to be referenced everywhere.
     
  2. jcsd
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