Question

Please provide clear steps, I'm a little confused about how to solve this question. Thanks.

Problem 2. (20 points) Particle in a magnetic field. The Hamiltonian for a particle of mass m and charge e in arn electronnagnetic field with scalar potential φ(r,t) and vector potential . (r,t) is given by where φ is the scalar potential and A is the vector potential. 2.1. (10 points) Show that the following transformation is canonical for any choice of the parameter o 0: 2P1 cos Q1-Q2) 2P sin Q1-P 2.2. (10 points) Apply this transformation to solve for the motion of a charged particle confined to a plane perpen- dicular to a constant magnetic field B × A and no electric field φ = 0, by: İ expressing the Hamiltonian in terms of (Q, P); choosing a to simplify the resulting expressions, i solving for Q(t) and P(t); and iv) transforming back to the original coordinates. What is the shape of the resulting curve?

Answer 1