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Hamilton's equation from heisenberg equation of motion

  1. Sep 6, 2014 #1
    I was wondering how to derive hamilton's equation (in the form of poisson brackets) from heisenberg's equation of motion
     
  2. jcsd
  3. Sep 6, 2014 #2

    ChrisVer

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    Gold Member

    change the commutation to anticommutation [with some i and hbar factors], and there you go...
     
  4. Sep 13, 2014 #3

    samalkhaiat

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    Science Advisor

    For any two operators [itex]\hat{ A }[/itex] and [itex]\hat{ B }[/itex], one can show that
    [tex]\mbox{ Lim }_{ \hbar \rightarrow 0 } \frac{ 1 }{ i \hbar } [ \hat{ A } , \hat{ B } ] = \{ A ( x , p ) , B ( x , p ) \}_{ PB } .[/tex]
    This is proved in

    https://www.physicsforums.com/showpost.php?p=1082430&postcount=7

    Sam
     
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