Hamilton's equation from heisenberg equation of motion

jelathome · Sep 6, 2014

I was wondering how to derive hamilton's equation (in the form of poisson brackets) from Heisenberg's equation of motion

ChrisVer · Sep 6, 2014

change the commutation to anticommutation [with some i and hbar factors], and there you go...

samalkhaiat · Sep 13, 2014

jelathome said:

I was wondering how to derive hamilton's equation (in the form of poisson brackets) from Heisenberg's equation of motion

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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