- #1

dyn

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I have been looking at canonical transformation using generating functions. I am using the Goldstein book and it gives the following example -

F1=qQ ⇔ Q=p and P=-q

F2=qP ⇔ Q=q and P=p

F3=pQ ⇔ Q=-q and P=-p

F4=pP ⇔ Q=p and P=-q

I'm confused ! Obviously functions 1 and 4 give the same canonical transformation Q=p and P=-q but functions 2 and 3 both return different transformations.

Are all 4 functions supposed to return the same transformation ?