Classical and quantum sextic anharmonic oscillators: Second-order solutions and the classical limit

摘要

We first use the Poincare-Linstedt method to solve the sextic anharmonic oscillator, up to the second order in the perturbation parameter, classically. Then, we derive the quantum solution, also up to the second order, considering the time evolution of the initial perturbed coherent states, in the framework of the Rayleigh-Schrodinger perturbation theory. Finally, enforcing appropriate initial conditions and taking h → 0, |α| → ∞ limit while h|α|~(1/2) is kept constant, we retrieve the classical perturbation series from the corresponding quantum solution.