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- Show that \begin{equation} Q= q\cos\theta - \frac{p}{m\omega} \sin\theta,\qquad P=m\omega q \sin\theta + p \cos\theta \end{equation} is a canonical transformation
- (i) by evaluating \([Q,P]_{q,p}\)
- (ii) by expressing \(pdq-PdQ\) as an exact differential \(dF_1(q,Q,t)\).Hence find the type 1 generating function of the transformation. To do this you must first express \(p,P\) in terms of \(q,Q\).
- Use the relation \(F_2=F_1+PQ\) to find the type 2 generating function \(F_2(q,P)\), and check your result by showing that \(F_2\) indeed generates the transformation.
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