Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials

2001/10/13 by Michael Christ, M. Christ, Christ, M. +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #34L40 #35P25 #42B20 #81Q10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34L40 #msc:35P25 #msc:42B20 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math/0110140

46 pages

arxiv created 2001/10/13 · openalex publication_date 2001/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove existence of modified wave operators for one-dimensional Schrödinger equations with potential in L^p(\reals), p<2. If in addition the potential is conditionally integrable, then the usual Möller wave operators exist. We also prove asymptotic completeness of these wave operators for some classes of random potentials, and for almost every boundary condition for any given potential.

Cited by

• One sided orthogonal polynomials and a pointwise convergence result for SU(2)-valued nonlinear Fourier series

Related

• Wave equation with slowly decaying potential: asymptotics and wave operators
• Scattering Theory of Schrödinger Operators with Random Sparse Potentials
• L^p Boundedness of the Scattering Wave Operators of Schroedinger Dynamics with Time-dependent Potentials and applications
• Wave operators on Sobolev spaces
• Scattering theory for Schrodinger equations with time-dependent short-range potentials via wave packet transform