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

被引：22

作者：

Celeghini, E. ^{[1
,2
]}

Kuru, S. ^{[3
]}

Negro, J. ^{[4
]}

del Olmo, M. A. ^{[4
]}

机构：

[1] Univ Florence, Dept Fis, I-50019 Florence, Italy

[2] INFN Sez Firenze, I-50019 Florence, Italy

[3] Ankara Univ, Fac Sci, Dept Phys, TR-06100 Ankara, Turkey

[4] Univ Valladolid, Dept Fis Teor Atom & Opt, E-47011 Valladolid, Spain

来源：

ANNALS OF PHYSICS | 2013年 / 332卷

关键词：

Superintegrable system; Higher order symmetry operator; Ladder operator; Classical motion; Trajectory; Constant of motion; SUPERINTEGRABILITY; POTENTIALS;

D O I：

10.1016/j.aop.2013.01.008

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：27 / 37

页数：11

共 23 条

[1] Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles [J].

Ballesteros, Angel ;

Enciso, Alberto ;

Herranz, Francisco J. ;

Ragnisco, Orlando .

ANNALS OF PHYSICS, 2009, 324 (06) :1219-1233

[2] Algebraic Aspects of Tremblay-Turbiner-Winternitz Hamiltonian Systems [J].

Calzada, J. A. ;

Celeghini, E. ;

del Olmo, M. A. ;

Velasco, M. A. .

7TH INTERNATIONAL CONFERENCE ON QUANTUM THEORY AND SYMMETRIES (QTS7), 2012, 343

[3] Dynamical algebras of general two-parametric Poschl-Teller Hamiltonians [J].

Calzada, J. A. ;

Kuru, S. ;

Negro, J. ;

del Olmo, M. A. .

ANNALS OF PHYSICS, 2012, 327 (03) :808-822

[4] On the superintegrability of TTW model [J].

Conera, Cezary .

PHYSICS LETTERS A, 2012, 376 (35) :2341-2343

[5] SUPERINTEGRABILITY IN CLASSICAL MECHANICS [J].

EVANS, NW .

PHYSICAL REVIEW A, 1990, 41 (10) :5666-5676

[6] Group approach to the factorization of the radial oscillator equation [J].

Fernandez, DJ ;

Negro, J ;

delOlmo, MA .

ANNALS OF PHYSICS, 1996, 252 (02) :386-412

[7] Integrable generalizations of oscillator and Coulomb systems via action-angle variables [J].

Hakobyan, T. ;

Lechtenfeld, O. ;

Nersessian, A. ;

Saghatelian, A. ;

Yeghikyan, V. .

PHYSICS LETTERS A, 2012, 376 (05) :679-686

[8] Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential [J].

Hussin, Veronique ;

Marquette, Ian .

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2011, 7

[9] THE FACTORIZATION METHOD [J].

INFELD, L ;

HULL, TE .

REVIEWS OF MODERN PHYSICS, 1951, 23 (01) :21-68

[10] Superintegrability and higher order integrals for quantum systems [J].

Kalnins, E. G. ;

Kress, J. M. ;

Miller, W., Jr. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (26)

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