Semiclassical Dynamics¶with Exponentially Small Error Estimates

Abstract:

We construct approximate solutions to the time–dependent Schrödinger¶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.