Coherent states of an accelerated particle

TL;DR

This paper constructs generalized coherent states for a massive accelerated particle, advancing the understanding of quantum states with unbounded motion and continuous spectra, and explores their representations and properties.

Contribution

It introduces a method to construct GCS for an accelerated particle, linking non-stationary and stationary states, and analyzes their representations in detail.

Findings

Complete set of non-stationary states expressed via elementary functions

Connection established between non-stationary and stationary states

Different representations of coherent states analyzed in detail

Abstract

We construct generalized coherent states (GCS) of a massive accelerated particle. This example is an important step in studying coherent states (CS) for systems with an unbounded motion and a continuous spectrum. First, we represent quantum states of the accelerated particle both known and new ones obtained by us using the method of non-commutative integration of linear differential equations. A complete set of non-stationary states for the accelerated particle is obtained. This set is expressed via elementary functions and is characterized by a continuous real parameter $\eta$, which corresponds to the initial momentum of the particle. A connection is obtained between these solutions and stationary states, which are determined by the Airy function. We solved the problem of constructing GCS, in particular, semiclassical states describing the accelerated particle, within the framework of the consistent method of integrals of motion. We have found different representations, coordinate one and in a Fock space, analyzing in detail all the parameters entering in these representations.