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Question

Mathematical Physics Question on Functions

If F1(Q,q)=QqF_1(Q, q) = Qq is the generating function of a canonical transformation from (p,q)(p, q) to (P,Q)(P, Q), then which one of the following relations is correct?

A

pP=Qq\frac{p}{P} = \frac{Q}{q}

B

Pp=Qq\frac{P}{p} = \frac{Q}{q}

C

pP=−Qq\frac{p}{P} = -\frac{Q}{q}

D

Pp=−Qq\frac{P}{p} = -\frac{Q}{q}

Answer

pP=−Qq\frac{p}{P} = -\frac{Q}{q}

Explanation

Solution

The correct option is (C) :pP=−Qq\frac{p}{P} = -\frac{Q}{q}