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I encountered three conserative theorem in textbook

One of conserative theorem is involving my question.

Liboff defined displacement operator as [itex] \hat{D}(\varsigma) = e^(\frac{i\varsigma\hat{p}_{x}}{\hbar}f(x) = f(x + \varsigma ) [/itex] but is it right?

If system is displaced from x to [itex] x + \varsigma [/itex], function f should be displaced

such as [itex] f(x - \varsigma) [/itex], it is function displacement from x to [itex] x + \varsigma [/itex]

Why liboff defined displacement operator in that way?

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# [Q]Conserative theorem and parity

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