Hi
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 ?
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 ?