Exact solutions of time-dependent three-generator systems

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dc.creatorShen, Jian-Qi
dc.creatorZhu, Hong-Yi
dc.creatorChen, Pan
dc.date2002-05-27
dc.date.accessioned2026-07-07T06:04:15Z
dc.date.available2026-07-07T06:04:15Z
dc.descriptionThere exist a number of typical and interesting systems or models which possess three-generator Lie-algebraic structure in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra $sl(2,C)$ or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schrödinger equations governing various three-generator quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, we show that the exact solutions can 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 that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors in time-dependent systems is briefly discussed.
dc.description16 pages,no figer
dc.identifierhttps://arxiv.org/abs/quant-ph/0205170
dc.identifierhttp://arxiv.org/abs/quant-ph/0205170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/90230
dc.subjectQuantum Physics
dc.titleExact solutions of time-dependent three-generator systems
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