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

DOI10.1142/S0129055X93000188zbMath0831.35145MaRDI QIDQ4289622

Tohru Ozawa, Arne Jensen

Publication date: 15 February 1996

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

time dependent Schrödinger equationexistence of wave operatorsunitarity of wave operators

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (12)

Results in \(L^ p({\mathbb{R}}^ d)\) for the Schrödinger equation with a time-dependent potential ⋮ On inverse scattering problem for the Schrödinger equation with repulsive potentials ⋮ Asymptotic completeness for long-range many-particle systems with Stark effect. II ⋮ Existence and nonexistence of wave operators for time-decaying harmonic oscillators ⋮ Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials ⋮ Long-range scattering for three-body Stark Hamiltonians ⋮ Critical scattering in a time-dependent harmonic oscillator ⋮ Unnamed Item ⋮ Asymptotic completeness for \(N\)-body quantum systems with long-range interactions in a time-periodic electric field ⋮ Scattering theory for the Schrödinger equation with repulsive potential ⋮ Unnamed Item ⋮ Scattering in an external electric field asymptotically constant in time

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