Time boundedness of the energy for the charge transfer model
type: Item
instance of: scholarly article
title: Time boundedness of the energy for the charge transfer model
zbMATH Open document ID: 0705.35117
DOI: 10.1007/BF02096499
author: Ulrich Wüller
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: The Schrödinger equation \(id\psi /dt=H(t)\psi\) in the space \(H^ 2({\mathbb{R}}^{\nu})\) is investigated where \(H(t)=-\Delta /2m+V(t)\), \(V(t)=\sum^{N}_{1}V_ j(x-y_ j(t))\), with the classical trajectories \(y_ j(t)\) given in advance and satisfying \(d^ 2y_ j/dt^ 2\in L_ 1({\mathbb{R}})\), \(| y_ j(t)-y_ k(t)| \geq \alpha t\) \((t>const.\), \(\alpha >0\), \(j\neq k)\). The potential V is subjected to certain weak requirements (which cannot be stated here), in particular the gradients \(\nabla V_ j\) are assumed to be bounded and integrable outside a compact set. Result: the time evolution \(\psi\) (t) has a uniformly bounded energy expectation, \(\sup (\psi (t),H(t)\psi (t))<\infty\), \(t>const\).
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 4157118
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: uniformly bounded energy expectation
MaRDI profile type: Publication
cites work: Q3665729
cites work: Q3940332
cites work: Q3756006
cites work: Q4066072
cites work: Q3732126
cites work: Q3822614
cites work: A multi-channel scattering theory for some time dependent Hamiltonians, charge transfer problem
cites work: Existence of solutions for Schrödinger evolution equations
description: scientific article; zbMATH DE number 4157118