Bound states and propagating states for time-dependent Hamiltonians. (English) Zbl 0532.47007
The definition of bound states and propagating states for quantum mechanical time-dependent Hamiltonians are suggested. The authors give a geometrical characterization of the above states and generalize many ”time-independent results” to the time-dependent case, e.g. a theorem of Ruelle. Most results concern the time-periodic case. The constructions for the Schrödinger operators are studied by D. R. Yafaev [see e.g. Mat. Sb., Nov. Ser. 118(160), 262-279 (1982; Zbl 0492.35059)].
Reviewer: M.A.Perelmuter
MSC:
| 47A40 | Scattering theory of linear operators |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 35P25 | Scattering theory for PDEs |
Keywords:
bound states and propagating states for quantum mechanical time-dependent Hamiltonians; time-periodic caseCitations:
Zbl 0492.35059References:
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