1998/12/23 by George A. Hagedorn, Alain Joye · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:81Q05
paper · pdf · doi:10.1007/s002200050732
arxiv created 1998/12/23 · openalex publication_date 1999/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We construct approximate solutions to the time--dependent Schrödinger equation i ℏ (∂ ψ)/(∂ t) = - (ℏ2)/2 Δψ+ V ψ for small values of ℏ. 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/ℏ, for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T', |t|≤ T' |log(ℏ)| implies the norms of the errors are bounded by C' exp-γ'/ℏσ, for some C', γ'>0, and σ>0.