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- W2023341413 abstract "This paper studies the time evolution of state vectors that are the solutions of the time-dependent Schrödinger equation, characterized by a Hamiltonian h. We employ trace-theorem methods to prove that the transit time of state vectors through a finite space region, Σ, may be used to construct a family in the energy variable, ϵ, of unique, positive, trace-class operators. The matrix elements of these operators give the transit time of any vector through Σ. It is proved that the trace of these operators, for a fixed energy ϵ, provide a function which simultaneously gives the sum of all orbital transit times through region Σ and represents the state density of all vectors that have support on Σ and energy ϵ. We use the transit-time operators to recover the usual theory of time delay for single-channel scattering systems. In the process we extend the known results on time delay to include scattering by fixed impurities in a periodic medium." @default.
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- W2023341413 date "1980-04-01" @default.
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- W2023341413 title "Transit time measures in scattering theory" @default.
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- W2023341413 doi "https://doi.org/10.1016/0003-4916(80)90370-x" @default.
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