A unified approach to quantum and classical TTW systems based on factorizations

Celeghini E., KURU Ş., Negro J., del Olmo M. A.

ANNALS OF PHYSICS, vol.332, pp.27-37, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 332
  • Publication Date: 2013
  • Doi Number: 10.1016/j.aop.2013.01.008
  • Journal Name: ANNALS OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.27-37
  • Keywords: Superintegrable system, Higher order symmetry operator, Ladder operator, Classical motion, Trajectory, Constant of motion, SUPERINTEGRABILITY, POTENTIALS
  • Ankara University Affiliated: Yes

Abstract

A unifying method based on factorization properties is introduced for finding symmetries of quantum and classical superintegrable systems using the example of the Tremblay-Turbiner-Winternitz (TTW) model. It is shown that the symmetries of the quantum system can be implemented in a natural way to its classical version. Besides, by this procedure we get also other type of constants of motion depending explicitly on time that allow to find directly the motion of the system whose corresponding trajectories coincide with those obtained previously by using its symmetries. (C) 2013 Elsevier Inc. All rights reserved.