TY - JOUR
T1 - A unified approach to Schrödinger evolution of superoscillations and supershifts
AU - Aharonov, Yakir
AU - Behrndt, Jussi
AU - Colombo, Fabrizio
AU - Schlosser, Peter
N1 - Funding Information:
We are indebted to the anonymous referees for helpful suggestions and improvements. J. Behrndt and P. Schlosser gratefully acknowledge financial support by the Austrian Science Fund (FWF): P 33568-N. This publication is based on work from COST Action CA 18232 MAT-DYN-NET, supported by COST (European Cooperation in Science and Technology), www.cost.eu .
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/3
Y1 - 2022/3
N2 - Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green’s function, but not its explicit form. With this efficient general technique, we are able to treat various potentials.
AB - Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green’s function, but not its explicit form. With this efficient general technique, we are able to treat various potentials.
KW - Green’s function
KW - Schrödinger equation
KW - Superoscillating function
KW - Supershift property
UR - http://www.scopus.com/inward/record.url?scp=85126176950&partnerID=8YFLogxK
U2 - 10.1007/s00028-022-00770-1
DO - 10.1007/s00028-022-00770-1
M3 - Article
AN - SCOPUS:85126176950
SN - 1424-3199
VL - 22
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 1
M1 - 26
ER -