Wavepacket Solutions of the Klein-Gordon Equation

TL;DR

This paper presents dispersion-free wavepacket solutions to the Klein-Gordon equation, characterized by a velocity parameter, and introduces a velocity operator linked to classical generators via canonical transformations.

Contribution

It introduces a new class of wavepacket solutions with a velocity operator that is linked to classical generators through canonical transformations.

Findings

Wavepacket solutions are dispersion-free and parameterized by velocity.

The velocity operator has commuting components and is symmetric in a scalar product space.

The velocity operator corresponds to a classical generator obtained by canonical transformation.

Abstract

We find dispersion-free wavepacket solutions to the Klein-Gordon equation, with the only free parameter being the wavepacket velocity $ {\bf v} $. These wavefunctions are eigenvectors of a velocity operator with commuting components which is symmetric in a certain scalar product space. We show that this velocity operator corresponds to a classical generator which may be obtained by a canonical tranformation from $ {\bf x}, {\bf k} $.