Coherent states of non-relativistic electron in magnetic-solenoid field

TL;DR

This paper constructs two types of coherent states for a nonrelativistic electron in a combined magnetic and Aharonov-Bohm field, showing they follow classical trajectories and are useful for semi-classical analysis.

Contribution

It introduces a new set of coherent states specific to the magnetic-solenoid field, extending known states to this combined field configuration.

Findings

Coherent states follow classical trajectories embracing or avoiding the solenoid.

States maintain their form during time evolution.

States reduce to Malkin-Man'ko coherent states without Aharonov-Bohm field.

Abstract

We construct coherent states of a nonrelativistic electron in the magnetic-solenoid field, which is a superposition of the Aharonov-Bohm field and a collinear uniform magnetic field. In the problem under consideration there are two kind of coherent states, the first kind corresponds to classical trajectories which embrace the solenoid and the second one to trajectories which do not. Mean coordinates in the constructed coherent states are moving along classical trajectories, the coherent states maintain their form under the time evolution, and represent a complete set of functions, which can be useful in semi classical calculations. In the absence of the Aharonov-Bohm filed these states are reduced to the well-known in the case of uniform magnetic field Malkin-Man'ko coherent states.