  We develop a complete analytical description of the time evolution of
squeezed states of a charged particle under the Fock-Darwin Hamiltonian and a
time-dependent electric field. This result generalises a relation obtained by
Infeld and Pleba\'nski for states of the one-dimensional harmonic oscillator.
We relate the evolution of a state-vector subjected to squeezing to that of
state which is not subjected to squeezing and for which the time-evolution
under the simple harmonic oscillator dynamics is known (e.g. an eigenstate of
the Hamiltonian). A corresponding relation is also established for the Wigner
functions of the states, in view of their utility in the analysis of cold-ion
experiments. In an appendix, we compute the response functions of the FD
Hamiltonian to an external electric field, using the same techniques as in the
main text.
