Again on coherent states in magnetic-solenoid field

TL;DR

This paper completes the analysis of coherent states in a combined magnetic-solenoid field, establishing their completeness and comparing them to known states in pure magnetic fields, advancing understanding of quantum states in complex magnetic configurations.

Contribution

It proves nontrivial completeness relations for coherent states in magnetic-solenoid fields and compares these states with classical Malkin-Man'ko states in pure magnetic fields.

Findings

Established completeness relations for non-relativistic and relativistic coherent states.

Solved the Stieltjes moment problem for these states.

Provided a comparative analysis with Malkin-Man'ko coherent states.

Abstract

This article completes our study of coherent states in the so-called magnetic-solenoid field (a colinear combination of a constant uniform magnetic field and Aharonov-Bohm solenoid field) presented in JPA 2010 and 2011. Here we succeeded to prove nontrivial completeness relations for non-relativistic and relativistic coherent states in such a field. In addition, we solve here the relevant Stieltjes moment problem and present a comparative analysis of our coherent states and the well-known in the case of pure uniform magnetic field Malkin-Man'ko coherent states.