11 citations · 11 across the 2 of their papers we have counts for
6 papers · 1 filter
Inverse scattering for -body time-decaying harmonic oscillators
Atsuhide Ishida
In the previous study (Ishida, 2025), the author proved the uniqueness of short-range potential functions using the Enss-Weder time-dependent method (Enss and Weder, 1995) for a tw…
Threshold between short and long-range potentials for non-local Schrödinger operators
Atsuhide Ishida, Kazuyuki Wada
We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power with . In particula…
Critical scattering in a time-dependent harmonic oscillator
Atsuhide Ishida, Masaki Kawamoto
Controlled time-decaying harmonic oscillator changes the threshold of decay order of the potential functions in order to exist the physical wave operators. This threshold was first…
Inverse scattering in Stark effect
Atsuhide Ishida
We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and…
Existence and nonexistence of wave operators for time-decaying harmonic oscillators
Atsuhide Ishida, Masaki Kawamoto
Controlled time-decaying harmonic potentials decelerate the velocity of the charged particle but the particle never be trapped by this harmonic potentials. This physical phenomena…
Nonexistence of usual wave operators for fractional Laplacian and slowly decaying potentials
Atsuhide Ishida
We consider quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials. When a slowly decaying potential function is given, we prov…