The effective Hamiltonian which governs the propagation dynamics of nonspreading wave packets

Abstract: We discuss the propagation dynamics of nonspreading wave packets. We decompose the Hamiltonian into two parts. The first part is such that wave packets is its instantaneous eigenstate and is therefore irrelevant to the propagation of the packet. The second part is shown to be the effective Hamiltonian governing the motion of the packet both classically and quantum mechanically. Thus, analogous to Ehrenfest's theorem, nonspreading wave packets offer another view point directly connecting quantum mechanics and classical mechanics. This analysis also works for non-square-integrable packets, such as Airy packets.