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1 Virginia Tech Blacksburg 2 IF - Institut Fourier

Abstract : We construct approximate solutions to the time–dependent Schrödinger equation i ¯ h ∂ψ ∂t = − ¯ h 2 2 ∆ ψ + V ψ for small values of ¯ h. If V satisfies appropriate analyticity and growth hypotheses and |t| ≤ T , these solutions agree with exact solutions up to errors whose norms are bounded by C exp { − γ-¯ h } , for some C and γ > 0. Under more restrictive hypotheses, we prove that for sufficiently small T ′ , |t| ≤ T ′ | log¯ h| implies the norms of the errors are bounded by C ′ exp − γ ′ -¯ h σ , for some C ′ , γ ′ > 0, and σ > 0.

Keywords : Semiclassical methods quantum dynamics exponential asymptotics





Autor: George A. Hagedorn - Alain Joye -

Fuente: https://hal.archives-ouvertes.fr/



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