Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

被引：13
作者：
Calzada, J. A. [1 ]
Kuru, S. [2 ]
Negro, J. [3 ]
del Olmo, M. A. [3 ]
机构：
[1] Univ Valladolid, Dept Matemat Aplicada, Escuela Super Ingn Ind, E-47011 Valladolid, Spain
[2] Ankara Univ, Dept Phys, Fac Sci, TR-06100 Ankara, Turkey
[3] Univ Valladolid, Dept Fis Teor Atom & Opt, Fac Ciencias, E-47011 Valladolid, Spain
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2008年 / 41卷 / 25期
关键词：
D O I：
10.1088/1751-8113/41/25/255201
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2, 1) Lie algebra and determine the Hamiltonians through the Casimir operators. By means of discrete symmetries a broader set of operators is obtained closing a so(4, 2) algebra. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of unitary representations of su(2, 1) and so(4, 2).
引用
收藏
页数：11
相关论文
共 20 条
  • [1] ALGEBRAIC TREATMENT OF 2ND POSCHL-TELLER, MORSE-ROSEN AND ECKART EQUATIONS
    BARUT, AO
    INOMATA, A
    WILSON, R
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1987, 20 (13): : 4083 - 4096
  • [2] Superintegrable quantum u(3) systems and higher rank factorizations
    Calzada, JA
    Negro, J
    del Olmo, MA
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (04)
  • [3] Classical superintegrable SO(p,q) Hamiltonian systems
    Calzada, JA
    delOlmo, MA
    Rodriguez, MA
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 1997, 23 (01) : 14 - 30
  • [4] Pseudo-orthogonal groups and integrable dynamical systems in two dimensions
    Calzada, JA
    del Olmo, MA
    Rodríguez, MA
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1999, 40 (01) : 188 - 209
  • [5] Contraction of superintegrable Hamiltonian systems
    Calzada, JA
    Negro, J
    del Olmo, MA
    Rodríguez, MA
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (01) : 317 - 336
  • [6] INTEGRABLE SYSTEMS BASED ON SU(P,Q) HOMOGENEOUS MANIFOLDS
    DELOLMO, MA
    RODRIGUEZ, MA
    WINTERNITZ, P
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1993, 34 (11) : 5118 - 5139
  • [7] The conformal group SU(2,2) and integrable systems on a Lorentzian hyperboloid
    DelOlmo, MA
    Rodriguez, MA
    Winternitz, P
    [J]. FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 1996, 44 (03): : 199 - 233
  • [8] Two families of superintegrable and isospectral potentials in two dimensions
    Demircioglu, B
    Kuru, S
    Önder, M
    Verçin, A
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (05) : 2133 - 2150
  • [9] SUPERINTEGRABILITY OF THE WINTERNITZ SYSTEM
    EVANS, NW
    [J]. PHYSICS LETTERS A, 1990, 147 (8-9) : 483 - 486
  • [10] SUPERINTEGRABILITY IN CLASSICAL MECHANICS
    EVANS, NW
    [J]. PHYSICAL REVIEW A, 1990, 41 (10): : 5666 - 5676
12