Semiclassical Dynamics¶with Exponentially Small Error Estimates |
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| Authors: | George A Hagedorn Alain Joye |
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| Institution: | (1) Department of Mathematics and Center for Statistical Mechanics and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA, US;(2) Institut Fourier, Unité Mixte de Recherche CNRS-UJF 5582, Université de Grenoble I, BP 74, 38402 Saint Martin d'Hères Cedex, France, FR |
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| Abstract: | We construct approximate solutions to the time–dependent Schr?dinger?equation
for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T
′, implies the norms of the errors are bounded by for some C
′, γ′>0, and σ > 0.
Received: 7 January 1999 / Accepted: 30 April 1999 |
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