Resonances of the system of a particle in an oscillating spherical cavity

We study the resonances of the system of a particle in an infinite spherical well with an oscillating wall. Parametric resonances emerge when the oscillation frequency is equal to the energy difference between two eigenstates of the static cavity. Whereas an analytic calculation based on a two-level system approximation reproduces the numerical results at low driving amplitudes $\epsilon$, we observe a drastic change of behavior when $\epsilon >0.1\mathrm{}$, when new resonance states appear bearing no apparent relation to the eigenstates of the static system.