We show that three real-valued parameters govern the quantum motion of
an ion stored in the Paul trap. These parameters are two angles of ro
tation in phase space and a squeezing parameter. The time dependence o
f these parameters simplifies considerably using Floquet solutions. Th
is allows us to use the method of quantum state endoscopy to measure a
pure state of the vibratory motion of an ion taking into account the
full time dependence of the trapping potential.