Determine the Hamitonian and the value of so that the transformation is canonical.
Consider a transformation from coordinates ((q, p)) to new coordinates ((Q, P)) given by some functions (Q = Q(q,p)) and (P = P(q,p)). For a transformation to be canonical, it must preserve the form of Hamilton's equations. This is equivalent to requiring that the Poisson bracket satisfies: [ {Q, P} = 1, \quad {Q, Q} = _____ _____ ________ ______ _____ _________ ___ __________ _____ _________.
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