Wavepacket trains of a Paul trapped ion

By using Husimi’s test-function method, we construct n exact solutions of a single Paul trapped ion modelled by a quantum harmonic oscillator with a time-dependent ‘spring constant’. Any n th solution is a combination of the Fock state and coherent state, which describes a wavepacket train consisting of n + 1 packets. Its centre oscillates like the classical harmonic oscillator with variable frequency, while the width and height of each packet change simultaneously. When the deformation is small, it behaves like a propagated and non-deformed train, and the large deformation is identified with breathing of the wavepacket train.