2005-53.md

course	course_year	question_number	tags	title	year
Classical Dynamics	II	53	II 2005 Classical Dynamics	4.I.9C	2005

Define a canonical transformation for a one-dimensional system with coordinates $(q, p) \rightarrow(Q, P)$. Show that if the transformation is canonical then ${Q, P}=1$.

Find the values of constants $\alpha$ and $\beta$ such that the following transformations are canonical: (i) $Q=p q^{\beta}, P=\alpha q^{-1}$. (ii) $Q=q^{\alpha} \cos (\beta p), P=q^{\alpha} \sin (\beta p)$.