On coherence lengths of wave packets

TL;DR

This paper investigates the coherence lengths of quantum wave packets, analyzing their formation, stability, and transformations, emphasizing their finite spatial size and superposition nature compared to simple plane waves.

Contribution

It provides a detailed study of coherence lengths in coordinate and momentum space, highlighting the superposition nature of wave packets and their physical properties.

Findings

Wave packets are superpositions of plane waves with finite coherence lengths.

Coherence lengths vary depending on formation mechanisms and stability conditions.

Wave packets serve as approximate eigenstates of the free Hamiltonian.

Abstract

Coherence lengths of one particle states described by quantum wave functions are studied. We show that one particle states in various situations are not described by simple plane waves but are described by wave packets that are superpositions of plane waves. Wave packet is an approximate eigenstate of the free Hamiltonian and has a finite spatial size which we call the coherence length. The coherence lengths in the coordinate space and in the momentum space are studied in the present paper. We investigate several mechanisms of forming wave packets, stabilities of wave packets, and transformations of wave packets.