Application of polynomial su(1,1) algebra to Poschl-Teller potentials

作者：Zhang, Hong-Biao^*; Lu, Lu

来源：Journal of Mathematical Physics, 2013, 54(12): 122102.

DOI：10.1063/1.4834616

• NONLINEAR DEFORMATION ALGEBRA
• COHERENT STATES
• SU(2) ALGEBRA
• DYNAMICAL SYMMETRIES
• SPHERICAL GEOMETRY
• PHYSICAL SYSTEM
• HIGGS ALGEBRA
• LIE-ALGEBRAS
• REALIZATIONS
• MODELS

Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Poschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators (K) over cap (perpendicular to) of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derived naturally from the polynomial su(1, 1) algebras built by us.

• 出版日期2013-12
• 单位东北师范大学