2008/10/09 by Shikuan Mao, Mao, Shikuan, Shu Nakamura +1
Engineering · Mathematics · Physics and Astronomy · #35A10 #35A21 #35Q40 #58J47 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP #msc:35A10 #msc:35A21 #msc:35Q40 #msc:58J47
paper · pdf · doi:10.48550/arxiv.0810.1577
15 pages
arxiv created 2008/10/09 · openalex publication_date 2008/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Schrödinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [Nakamura 2004]. We characterize the wave front set of the solutions to the equation in terms of the classical scattering data and the propagator of the unperturbed harmonic oscillator. In particular, we give a "recurrence of singularities" type theorem for the propagation of the period t=π.