Temporally stable Coherent states for a free magnetic Schr\"odinger operator

TL;DR

This paper constructs and analyzes four classes of temporally stable coherent states for a free magnetic Schrödinger operator, providing explicit statistical and algebraic characterizations relevant for quantum systems with magnetic fields.

Contribution

It introduces four novel classes of coherent states for a magnetic Schrödinger operator, detailing their algebraic structure and statistical properties.

Findings

Four classes of coherent states are explicitly constructed.

The dynamical algebra for each class is identified.

Statistical quantities for each class are calculated explicitly.

Abstract

Eigenfunctions and eigenvalues of the free magnetic Schr\"odinger operator, describing a spinless particle confined to an infinite layer of fixed width, are discussed in detail. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space. Four different classes of temporally stable coherent states associated to the operator are presented. The first two classes are derived as coherent states with one degree of freedom and the last two classes are derived with two degrees of freedom. The dynamical algebra of each class is found. Statistical quantities associated to each class of coherent states are calculated explicitely.