Canonical Transformations — Herbert Goldstein, Charles Poole, John Safko
Physics — Mechanics · canonical-transformations
Problem
We start with a time independent Hamiltonian Ho(q,p) and impose an external oscillating field making the Hamiltonian
H=Ho(q,p)−εsinωt
where ε and ω are given constants.
(a) How are the canonical equations modified?
(b) Find a canonical transformation that restores the canonical form of the equations of motion and determine the ``new'' Hamiltonian.
(c) Give a possible physical interpretation of the imposed field.