REALIZATION OF DYNAMICAL GROUP FOR A SYMMETRIC WELL POTENTIAL tan2(πx/a) AND ITS CONTROLLABILITY-Reference-Cited by-同舟云学术

REALIZATION OF DYNAMICAL GROUP FOR A SYMMETRIC WELL POTENTIAL tan2(πx/a) AND ITS CONTROLLABILITY

Published:2006-11-20 Issue:28n29 Volume:21 Page:5833-5843
ISSN:0217-751X
Container-title:International Journal of Modern Physics A
language:en
Short-container-title:Int. J. Mod. Phys. A

Author:

DONG SHI-HAI¹²,LOZADA-CASSOU M.¹,ARJONA L MARCO A.³

Affiliation:

1. Programa de Ingeniería Molecular, Instituto Mexicano del Petróleo, Lázaro Cárdenas 152, 07730 Mexico, D. F., Mexico

2. Departamento de Física, Esc. Sup. de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, México D. F., 07738, México

3. Instituto Tecnológico de la Laguna, Departamento de Ingeniería Eléctrica y Electrónica, 27000 Torreón, Coahuila, Mexico

Abstract

The exact solutions of quantum system with a symmetric well potential V(x) = D tan 2(πx/a) are obtained. The ladder operators are constructed directly from the normalized eigenfunctions with the factorization method. It is shown that these ladder operators satisfy the commutation relations of the generators for an su(1, 1) algebra. The infinitely deep square well and harmonic limits of this potential are briefly studied. The controllability of this system is also investigated. It is demonstrated that this system with discrete bound states can be strongly completely controlled. This may be realized theoretically by acting the creation operator [Formula: see text] on the ground state.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217751X06033015

Reference34 articles.

1. The Factorization Method

2. Closed‐form expressions of matrix elements and eigenfunctions from ladder‐operator considerations