We start with a time independent Hamiltonian Ho(q, p) and impose an external oscillating f...

We start with a time independent Hamiltonian Ho(q, p) and impose an external oscillating field making the Hamiltonian

where ε and ω are given constants.

(a) How are the canonical equations modified?

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(b) Find a canonical transformation that restores the canonical form of the equations of motion and determine the “new” Hamiltonian.

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(c) Give a possible physical interpretation of the imposed field.