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

TL;DR

This paper analyzes the Hamiltonian governing nonspreading wave packets, revealing an effective Hamiltonian that links quantum and classical dynamics, applicable even to non-square-integrable packets like Airy packets.

Contribution

It introduces a decomposition of the Hamiltonian to identify the effective Hamiltonian that governs nonspreading wave packet propagation, bridging quantum and classical mechanics.

Findings

Effective Hamiltonian governs wave packet motion.

Applicable to non-square-integrable packets like Airy packets.

Provides a new perspective connecting quantum and classical dynamics.

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.