In Dirac's book there is a displacement operator, $d_x$, which I conceived to be the same as derivative operator. But apparently it is not. What is the difference? They lead to different relations to the momentum listed in equation $(149)$ of here and $(217)$ of here.
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$\begingroup$ Comment to the question (v1): It would be good if OP (or somebody else?) could try to make the question formulation self-contained, so one doesn't have to open the links to understand the question. $\endgroup$– Qmechanic ♦Commented Sep 24, 2015 at 7:34
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$\begingroup$ Sorry for that, and sorry for asking so quickly. I just found the answer in Wikipedia. I will type it all up tonight! Thanks! $\endgroup$– Cat BranchmanCommented Sep 24, 2015 at 7:45
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The displacement operator shifts the wave function A(x) to A(x+dx)
answered Sep 24, 2015 at 5:21
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$\begingroup$ I think that is the translation operator which is different from Dirac's definition on displacement operator. $\endgroup$ Commented Sep 24, 2015 at 5:36