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- W67051874 abstract "We discuss various constructions of approximate solutions to the time–dependent Schrodinger equation i ~ ∂ψ ∂t = − ~ 2 2 ∆ψ + V ψ in IRd for small values of ~ by means of wave packets that are localized in position and momentum. After reviewing earlier constructions that yield approximations up to O(~) errors, we show that if V satisfies appropriate analyticity and growth hypotheses, similar constructions agree with exact solutions up to errors of order e γ/~ for some γ > 0, provided t belongs to some fixed, compact time interval. Under more restrictive hypotheses, we extend the validity of these exponential estimates up to the Ehrenfest time scale: For sufficiently small T , |t| ≤ T ′ | log(~)| implies that the norm of the error is of order e γ ′/~σ for some γ > 0, and σ > 0." @default.
- W67051874 created "2016-06-24" @default.
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- W67051874 date "2015-01-01" @default.
- W67051874 modified "2023-09-27" @default.
- W67051874 title "Semiclassical Dynamics and Exponential Asymptotics" @default.
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