Document Type
Article
Publication Date
3-14-2022
Abstract
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.
Recommended Citation
Aharonov, Y., Behrndt, J., Colombo, F. et al. A unified approach to Schrödinger evolution of superoscillations and supershifts. J. Evol. Equ. 22, 26 (2022). https://doi.org/10.1007/s00028-022-00770-1
Peer Reviewed
1
Copyright
The authors
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
This article was originally published in Journal of Evolution Equations, volume 22, in 2022. https://doi.org/10.1007/s00028-022-00770-1