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 {\it time-dependent} Schrödinger 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 {\it explicit} solutions may also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator ({\it i. e.}, the {\it 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.

11 pages, Latex. accepted by Euro. Phys. J. D

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