Coherent States for Discrete Spectrum Dynamics

TL;DR

This paper constructs and characterizes coherent states for systems with discrete spectra, exemplified by the hydrogen atom, satisfying key physical properties and providing a unique set of such states.

Contribution

It introduces a method to define coherent states for discrete spectrum systems, ensuring they meet physical criteria and are uniquely determined for the hydrogen atom.

Findings

Coherent states satisfy continuity, resolution of unity, stability, and action identity.

Unique coherent states are derived for the hydrogen atom.

The framework can be applied to other systems with discrete spectra.

Abstract

Coherent states for general systems with discrete spectrum, such as the bound states of the hydrogen atom, are discussed. The states in question satisfy: (1) continuity of labeling, (2) resolution of unity, (3) temporal stability, and (4) an action identity. This set of reasonable physical requirements uniquely specify coherent states for the (bound state portion of the) hydrogen atom.