Coherent states for a system of an electron moving in a plane: case of discrete spectrum

TL;DR

This paper constructs various classes of coherent states for an electron in a plane under magnetic and electric fields, focusing on the discrete spectrum and establishing their mathematical properties.

Contribution

It introduces new coherent states for a quantum system with both discrete and continuous spectra, expanding the understanding of such states in magnetic field contexts.

Findings

Successfully constructed coherent states satisfying key criteria.

Extended the framework to systems with mixed spectra.

Provided mathematical basis for future quantum state analysis.

Abstract

In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfies.