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TEMPORALLY STABLE COHERENT STATES FOR A FREE MAGNETIC SCHRÖDINGER OPERATOR

Kengatharam Thirulogasanthar, Nasser Saad, Attila B. von Keviczky

Published Jan 1, 2004• 3 citations
OpenAlex

Abstract

Abstract. Eigenfunctions and eigenvalues of the free magnetic Schrödinger 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. 1.

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Temporally stable coherent states for a free magnetic Schrödinger operator

K. Thirulogasanthar, Nasser Saad, Attila B. von Keviczky

Eigenfunctions and eigenvalues of the free magnetic Schrödinger 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 with 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 explicitly.

arXiv:math-ph/0404036•Journal of Mathematical Physics•Jun 9, 2004•2 citations

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

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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.

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COHERENT STATES WITH COMPLEX FUNCTIONS

Kengatharam Thirulogasanthar, G. Honnouvo

Abstract. The canonical coherent states are expressed as infinite series in powers of a complex number z in their infinite series version. In this article we present classes of coherent states by replacing this complex number z by other choices, namely, iterates of a complex function, higher functions and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states. 1.

•Jan 1, 2003•1 citation

Coherent States and the Magnetic Operators

A. D. Jannussis, Loucas C. Papaloucas

In the present paper a method of calculation of the density matrix in the Schrödinger picture is given, in terms of the known creation and annihiliation operators a+ and a. New magnetic operators are given with the help of the coherent states, which depend on two free parameters μ and ν. For the case μ=ν= (e H )/ (2 ħ c), these operators lead to the well-known magnetic operators, as they are given in the current litterature.

Zeitschrift für Naturforschung A•May 1, 1973•5 citations

BARUT–GIRARDELLO COHERENT STATES CONSTRUCTED BY Ym m(θ,φ) AND Ym+1 m(θ,φ) FOR A FREE PARTICLE ON THE SPHERE

Alireza Chenaghlou, Hossein Fakhri

Using the realization idea of simultaneous shape invariance with respect to two different parameters of the associated Legendre functions, the Hilbert space of spherical harmonics Yn m(θ,φ) corresponding to the motion of a free particle on a sphere is split into a direct sum of infinite-dimensional Hilbert subspaces. It is shown that these Hilbert subspaces constitute irreducible representations for the Lie algebra u (1,1). Then by applying the lowering operator of the Lie algebra u (1,1), Barut–Girardello coherent states are constructed for the Hilbert subspaces consisting of Ym m(θ,φ) and Ym+1 m(θ,φ).

Modern Physics Letters A•Nov 2, 2004•17 citations
Abstract. Eigenfunctions and eigenvalues of the free magnetic Schrödinger 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. 1.
Eigenfunctions and eigenvalues of the free magnetic Schrödinger 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 with 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 explicitly.
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.
Abstract. The canonical coherent states are expressed as infinite series in powers of a complex number z in their infinite series version. In this article we present classes of coherent states by replacing this complex number z by other choices, namely, iterates of a complex function, higher functions and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states. 1.
Using the realization idea of simultaneous shape invariance with respect to two different parameters of the associated Legendre functions, the Hilbert space of spherical harmonics Yn m(θ,φ) corresponding to the motion of a free particle on a sphere is split into a direct sum of infinite-dimensional Hilbert subspaces. It is shown that these Hilbert subspaces constitute irreducible representations for the Lie algebra u (1,1). Then by applying the lowering operator of the Lie algebra u (1,1), Barut–Girardello coherent states are constructed for the Hilbert subspaces consisting of Ym m(θ,φ) and Ym+1 m(θ,φ).