Dispersive Estimates for Schr�dinger Operators in Dimensions One and Three

2003/06/30 by Michael Goldberg, M. Goldberg, Wilhelm Schlag +1 · 230 citations
Mathematics · #Advanced Mathematical Physics Problems #Mathematical physics #Mathematics #Numerical methods in inverse problems #Physics #Quantum mechanics #Schrödinger's cat #Spectral Theory in Mathematical Physics #math.AP #msc:35Q40

paper · pdf · doi:10.1007/s00220-004-1140-5

published in Communications in Mathematical Physics 251(1), 157-178 (Springer Science+Business Media) · 20 pages. Corrected typos and improved explanatory remarks at the end

arxiv created 2004/03/19 · openalex publication_date 2004/08/26 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We prove L¹ --> L^∞ estimates for linear Schroedinger equations in dimensions one and three. The potentials are only required to satisfy some mild decay assumptions. No regularity on the potentials is assumed.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials
• Decay estimates for Schrödinger operators
• Inverse scattering on the line

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