How to find generating function of canonical transformation?
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Explanation:
For the generating function F1(q,Q), we have dF1/dq=p and p=Q/q
then
F1=Qln(q)+K1(Q)(1)
and also
dF1/dQ=−P(2)
and
P=ln(Q/q)−(1/2)ln(Q)(a)
substituting equation (a) in (2) and integrating
F1=−(1/2)(Qln(Q)−Q)+Qln(q)+K2(q)(3)
comparing (1) and (3) we get
F1=−(1/2)(Qln(Q)−Q)+Qln(q)
with
K2(q)=0 and K1(Q)=−(1/2)(Qln(Q)−Q)
(here d()/dq and d()/dQ actually stand for the partial derivatives with respect to q and Q)
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