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تسجيل مستخدم جديدSpectrum Generating Algebras for the free motion in $S^3$
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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.
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In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra
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