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HxWang

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**How to understand "momentum is the generator of translation" ?**

"As it is known from classical mechanics, the momentum is the generator of translation", it is from WIKI, (http://en.wikipedia.org/wiki/Momentum_operator)

I don't understand its meaning.

[itex] T(ε) [/itex] is translation operator, then [itex] T(ε)f(x)=f(x-ε)=f(x)-ε\frac{\partial f}{\partial x}=(1-ε \frac{\partial }{\partial x}) f(x) [/itex] ,

so [itex] T(ε)=1-ε \frac{\partial }{\partial x} = 1 + i ε (i \frac{\partial }{\partial x}) [/itex],

we can say [itex] i \frac{\partial }{\partial x} [/itex] is the generator of translation, where is momentum ??