EXISTENCE AND NON-EXISTENCE RESULTS FOR WAVE OPERATORS FOR PERTURBATIONS OF THE LAPLACIAN-Reference-Cited by-同舟云学术

EXISTENCE AND NON-EXISTENCE RESULTS FOR WAVE OPERATORS FOR PERTURBATIONS OF THE LAPLACIAN

Published:1993-09 Issue:03 Volume:05 Page:601-629
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

JENSEN ARNE¹²,OZAWA TOHRU³

Affiliation:

1. Department of Mathematics and Computer Science, Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7, DK-9220 Aalborg Ø, Denmark

2. Current address: Mittag-Leffler Institute, Auravägen 17, S-182 62 Djursholm, Sweden

3. Department of Mathematics, Hokkaido University, Sapporo 060, Japan

Abstract

Schrödinger operators with time-dependent potentials are studied. Necessary and sufficient conditions for existence of ordinary and Dollard-type modified wave operators are obtained. Sharp results for potentials with a specified leading term are obtained. Applications are given to the surfboard Schrödinger equation and to Stark Hamiltonians. In the latter case the discrepancy between classical and quantum scattering in dimension one is resolved.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X93000188

Cited by 11 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials;Journal of Mathematical Physics;2023-12-01

2. Critical scattering in a time-dependent harmonic oscillator;Journal of Mathematical Analysis and Applications;2020-12

3. Existence and Nonexistence of Wave Operators for Time-Decaying Harmonic Oscillators;Reports on Mathematical Physics;2020-06

4. On inverse scattering problem for the Schrödinger equation with repulsive potentials;Journal of Mathematical Physics;2014-08

5. Scattering in an external electric field asymptotically constant in time;Journal of Mathematical Physics;2011-06