Spectrum Generating Algebras for the free motion in $S^3$

Abstract

We construct the spectrum generating algebra (SGA) for a free particle in the three dimensional sphere $S^3$ for both, classical and quantum descriptions. In the classical approach, the SGA supplies time-dependent constants of motion that allow to solve algebraically the motion. In the quantum case, the SGA include the ladder operators that give the eigenstates of the free Hamiltonian. We study this quantum case from two equivalent points of view.

29 pages, 1 figure

References in corpus (2)

• Factorizations of one dimensional classical systems
• Kepler Problem in the Constant Curvature Space

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