Analyzing and constructing general nonspreading wave packets

TL;DR

This paper presents a method for constructing and analyzing general nonspreading wave packets, revealing how their shape and motion are governed by Hamiltonian decomposition and effective spatial shifting.

Contribution

It introduces a novel Hamiltonian decomposition approach to understand and construct nonspreading wave packets with arbitrary shape and motion.

Findings

Time evolution operator acts as a spatial shift.

Hamiltonian part changing the state governs wave packet motion.

Method enables construction of nonspreading wave packets with general properties.

Abstract

We show the method for constructing nonspreading wave packets whose shape and motion can be general. We analyze the time evolution of nonspreading wave packets by decomposing the Hamiltonian into two parts. Of the two, one changes the instantaneous state, the other does not. Through this decomposition, the time evolution operator is shown to be effectively a spatial shifting operator. This explains why nonspreading wave packets can be nonspreading. And we show that the part of the Hamiltonian which changes the instantaneous state governs the motion of the nonspreading wave packets.