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

Isiaka Aremua,Laure Gouba

doi:10.1088/2399-6528/ac40a4

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 satisfy.

Highlights

From a generalization of the definition of canonical coherent states, Gazeau and Klauder proposed a method to construct temporally stable coherent states for a quantum system with one degree of freedom [2]
In some previous works, motivated by these developments, multidimensional vector coherent states have been performed for Hamiltonians describing the nanoparticle dynamics in terms of a system of interacting bosons and fermions [6]; from a matrix formulation of the Landau problem and the corresponding Hilbert space, an analysis of various multi-matrix vector coherent states extended to diagonal matrix domains has been performed on the basis of Landau levels [7]
The motion of an electron in a noncommutative (x, y) plane, in a constant magnetic field background coupled with a harmonic potential has been examined with the relevant vector coherent states constructed and discussed [8]

Summary

Introduction

From a generalization of the definition of canonical coherent states, Gazeau and Klauder proposed a method to construct temporally stable coherent states for a quantum system with one degree of freedom [2]. Following the method developed in [2, 4], we investigate in a recent work [1] by considering Landau levels, various classes of coherent states as in [9, 5, 10] arising from physical. The present paper is a direct continuation of our work in reference [1], where we construct different classes of coherent states corresponding to the case of discrete spectrum.

Coherent states for shifted Hamiltonians with more than one degree of freedom

Coherent states of the shifted Hamiltonians

Coherent states with one degree of freedom

Coherent states with two degrees of freedom

Outlook