English

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}
}