(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the following transformation is canonical:

[itex]Q=\ln \left ( \frac{\sin p }{q} \right )[/itex], [itex]P=q \cot p[/itex].

2. Relevant equations

A transformation is canonical if [itex]\dot Q=\frac{\partial H'}{\partial P}[/itex] and [itex]\dot P =-\frac{\partial H'}{\partial Q}[/itex].

H' is the Hamiltonian in function of Q and P.

3. The attempt at a solution

I've calculated [itex]\dot Q = \dot p \cot p - \frac{\dot q \sin p }{q}[/itex] and [itex]\dot P=\dot q \cot p - \frac{q \dot p}{\sin ^2 p}[/itex].

Now I guess I must check out if the conditions about the partial derivatives of the Hamiltonian are satisfied but I do not know either H(q,p) nor do I know H'(Q,P). I'm stuck here.

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# Show that a transformation is canonical

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