2025/04/08 by Atsuhide Ishida, Ishida, Atsuhide · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2504.05915
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonians of quadratic type. The time-dependent coefficient on the repulsive term decays as the inverse square of time, which is the threshold between the standard free Schroedinger operator and the time-independent repulsive Hamiltonians of quadratic type. Applying the Enss-Weder time-dependent method, we can determine uniquely the short-range potential functions with Coulomb-like singularities from the velocity limit of the scattering operator.