By any method you choose, show that the following transformation is canonical: where α is...

By any method you choose, show that the following transformation is canonical:

where α is some fixed parameter.

Apply this transformation to the problem of a particle of charge q moving in a plane that is perpendicular to a constant magnetic field B. Express the Hamiltonian for this problem in the (Qi, Pi) coordinates letting the parameter α take the form

From this Hamiltonian, obtain the motion of the particle as a function of time.