TY - JOUR
T1 - Schrödinger evolution of superoscillations with delta- and delta'-potentials
AU - Behrndt, Jussi
AU - Aharonov, Yakir
AU - Colombo, Fabrizio
AU - Schlosser, Peter
PY - 2020
Y1 - 2020
N2 - In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with δ- and δ′-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space A1(C). Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under δ- and δ′-potentials
AB - In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with δ- and δ′-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space A1(C). Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under δ- and δ′-potentials
U2 - 10.1007/s40509-019-00215-4
DO - 10.1007/s40509-019-00215-4
M3 - Article
SN - 2196-5609
VL - 7
SP - 293
EP - 305
JO - Quantum Studies: Mathematics and Foundations
JF - Quantum Studies: Mathematics and Foundations
ER -