- Show that \begin{equation} Q=-p ,\qquad P=q + Ap^2 \end{equation} (where A is any constant) is a canonical transformation,
- (i) by evaluating \([Q,P]_{q,p}\)
- (ii) by expressing \(pdq-PdQ\) as an exact differential \(dF(q,Q)\). Hence find the type one generating function of the transformation. To do this, you must first use the transformation to 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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4727:Diamond Point
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