Reply to ‘‘Comment on ‘Exact solution of the wave dynamics of a particle bouncing chaotically on a periodically oscillating-wall’’’

Abstract

A reexamination of the results of my earlier paper [Phys. Rev. E 50, 3116 (1994)] is supplied using entirely straightforward methods, i.e., without appealing to operator formalism. This reexamination confirms the consistency of the work in that paper by extracting a term proportional to time that Dembrinski et al. [Phys. Rev. E 53, 4243 (1996)] claim is not present. The arguments of Dembinski et al. are not refuted, but it is pointed out that they are based upon methods within which one readily encounters paradoxes such [p${\mathrm{^}}^{2}$,p^]\ensuremath{\ne}0 and [x^,p^]\ensuremath{\ne}i^. The present exposition avoids such methods. Unfortunately I am not prepared to address their numerical results. This will have to await further investigation. However, an example of numerical results of my own is presented in order to illustrate the richness of the dynamics of the model. \textcopyright{} 1996 The American Physical Society.