The Schrodinger particle in an oscillating spherical cavity

We study a Schr¨odinger 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 ǫ , we observe a drastic change of behaviour when ǫ > 0 . 1, when new resonance states appear bearing no apparent relation to the eigenstates of the static system. We study in this article the behaviour of a Schr¨odinger particle confined in a spherical cavity with an oscillating boundary that constitutes a particular kind of time-dependent perturbation. Our study provides a conceptually simple “laboratory” in which the subtle and nontrivial aspects of the resonant coupling between the oscillating wall and a particle trapped inside the cavity can be investigated. Our original motivation in this work comes from our attempt to construct a dynamical bag model of hadrons [1]; however, our results may bear implications on the physics of a wide range of systems such as cavity QED [2] and perhaps even sonoluminescence [3].