Hamilton's equation from heisenberg equation of motion

jelathome
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I was wondering how to derive hamilton's equation (in the form of poisson brackets) from Heisenberg's equation of motion
 
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change the commutation to anticommutation [with some i and hbar factors], and there you go...
 
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 \hat{ A } and \hat{ B }, one can show that
\mbox{ Lim }_{ \hbar \rightarrow 0 } \frac{ 1 }{ i \hbar } [ \hat{ A } , \hat{ B } ] = \{ A ( x , p ) , B ( x , p ) \}_{ PB } .
This is proved in

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

Sam
 

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