A unified approach to exact solutions of time-dependent Lie-algebraic quantum systems
Abstract
By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the time-dependent Schr\"odinger equations which govern the various Lie-algebraic quantum systems in atomic physics, quantum optics, nuclear physics and laser physics are obtained. It is shown that the explicit solutions may also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator ( i. e., the time-independent invariant) for some quantum systems without quasi-algebraic structures. The global and topological properties of geometric phases and their adiabatic limit in time-dependent quantum systems/models are briefly discussed.
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