Unformatted text preview: F ∂ ∂p G∂ ∂p F ∂ ∂q G ³´ FG, where the subscript F (or G ) attached to a partial derivative indicates that the particular derivative applies to operator F (or G ). In the classical limit ¯ h → 0, we need to keep only the ﬁrst two terms in the exponential series, and GF = FGi ¯ h ² ∂F ∂q ∂G ∂p∂F ∂p ∂G ∂q ³ , i.e. 1 i ¯ h [ F,G ] = [ F,G ] P.B. , where [ F,G ] P.B. denotes the Poisson Bracket in classical mechanics. The operator derivatives are deﬁned as ∂F ( q,p ) ∂q = lim Δ q → 1 Δ q { F ( q + Δ q,p )F ( p,q ) } , where Δ q is an inﬁnitesimal cnumber....
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 '08
 ELSER, V
 mechanics, Derivative, Work, arbitrary operator, arbitrary operator functions, particular derivative applies

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