Nonlinear Dynamical Symmetries of Some Two-Dimensional  Quantum Systems

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Nonlinear Dynamical Symmetries of Some Two-Dimensional Quantum Systems

RUAN Dong^1,2,3 and SUN Hong-Zhou^1,3,4

¹ Department of Physics, Tsinghua University, Beijing 100084, China
² Key Laboratory of Quantum Information and Measurements of Ministry of Education, Tsinghua University, Beijing 100084, China
³ Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China
⁴ Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China

Received: 2004-03-05 Revised: 1900-01-01 Published: 2004-09-15
Contact: RUAN Dong

Abstract

Abstract: In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as the Kepler--Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalized pseudo-oscillators in the two-dimensional flat space. Their nonlinear spectrum generating algebras are shown to be relevant to polynomial angular momentum algebras.

Key words: nonlinear dynamical symmetry, polynomial angular momentum algebra, Kepler-Coulomb system, harmonic oscillator, pseudo-oscillator

PACS numbers:

11.30.Na

RUAN Dong,, and SUN Hong-Zhou,,, Commun. Theor. Phys. 42 (2004) 379.

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Nonlinear Dynamical Symmetries of Some Two-Dimensional Quantum Systems

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