2019/11/12 by Yakir Aharonov, Aharonov, Yakir, Jussi Behrndt +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1911.04693
openalex publication_date 2019/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 converges 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.