ISSN:
1434-6079
Keywords:
PACS. 03.65.-w Quantum mechanics – 03.65.Fd Algebraic methods – 42.50.Gy Strong-field excitation of optical transitions in quantum systems; multi-photon processes; dynamic Stark shift
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: There exist a number of typical and interesting systems and/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 both 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 Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown 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 and its adiabatic limit in time-dependent systems is briefly discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1140/epjd/e2003-00043-7
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