On the time-dependent solutions of the Schr?dinger's equation. II. the one-mode field perturbed harmonic oscillator

摘要

The solution of the time-dependent Schr?dinger's equation for a perturbed harmonic oscillator is obtained using a solvable Lie algebra. We choose a harmonic oscillator interacting with a one-mode field, where the perturbation happens to be periodic in time. This leads to one of the simplest Floquet problems. Using the Wei-Norman theorem, the Floquet wave function is obtained as well as the semiclassical Floquet shift in the energy.