Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type
Analysis of PDEs
2025-11-17 v4
Abstract
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.
Keywords
Cite
@article{arxiv.2504.05915,
title = {Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type},
author = {Atsuhide Ishida},
journal= {arXiv preprint arXiv:2504.05915},
year = {2025}
}