Abstract
The evolution of squeezed coherent states (CSs) of motion for trapped ions is investigated by applying the time dependent variational principle (TDVP) for the Schr\"{o}dinger equation. The method is applied in case of Paul and combined traps, for which the classical Hamiltonian and equations of motion are derived. Hence, CS provide a natural framework to: (a) engineer quantum correlated states for trapped ions intended for ultraprecise measurements, (b) explore the mechanisms responsible for decoherence, and (c) investigate the quantum-classical transition.