Boundedness of energy for N-body Schrödinger equations with time dependent small potentials

Fuente: arXiv
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Autor principal: Yajima, Kenji
Formato: Preprint
Publicado: 2024
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author Yajima, Kenji
author_facet Yajima, Kenji
contents We prove that Sobolev norms of solutions to time dependent Schrödinger equations for $d$-dimensional $N$-partcles interacting via time dependent two body potentials are bounded in time if certain Lebesgue norms of the potentials are small uniformly in time. The proof uses the scattering theory in the extended phase space which proves that all particles scatter freely in the remote past and far future.
format Preprint
id arxiv_https___arxiv_org_abs_2403_07400
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Boundedness of energy for N-body Schrödinger equations with time dependent small potentials
Yajima, Kenji
Analysis of PDEs
Mathematical Physics
35Q41
We prove that Sobolev norms of solutions to time dependent Schrödinger equations for $d$-dimensional $N$-partcles interacting via time dependent two body potentials are bounded in time if certain Lebesgue norms of the potentials are small uniformly in time. The proof uses the scattering theory in the extended phase space which proves that all particles scatter freely in the remote past and far future.
title Boundedness of energy for N-body Schrödinger equations with time dependent small potentials
topic Analysis of PDEs
Mathematical Physics
35Q41
url https://arxiv.org/abs/2403.07400