Inverse \(N\)-body scattering with the time-dependent Hartree-Fock approximation

DOI10.3934/IPI.2021002zbMath1467.35358arXiv1912.03462OpenAlexW3115602730MaRDI QIDQ2037223

Michiyuki Watanabe

Publication date: 30 June 2021

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.03462

zbMATH Keywords

Hartree-Fock approximationinverse scattering problemsquantum N-body scattering

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse scattering problems in quantum theory (81U40) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• On the existence of solutions to time-dependent Hartree-Fock equations
• Multidimensional inverse scattering for the nonlinear Klein-Gordon equation with a potential
• On small data scattering with cubic convolution nonlinearity
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• On inverse scattering for the \(N\)-body Schrödinger equation
• Multidimensional inverse problems in perturbed stratified media
• Linear integral equations.
• Structure of the resolvent for three-body potentials
• The \(L^{p}\)-\(L^{p'}\) estimate for the Schrödinger equation on the half-line
• Scattering theory for time-dependent Hartree-Fock type equation
• Time-dependent method for non-linear Schrödinger equations in inverse scattering problems
• Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential
• Multidimensional inverse scattering in an electric field
• The \(W_{k,p}\)-continuity of the Schrödinger wave operators on the line
• \(L^p\)-\(L^{\acute p}\) estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
• Inverse scattering for the non-linear Schrödinger equation: Reconstruction of the potential and the non-linearity
• Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case
• On multidimensional inverse scattering in time-dependent electric fields
• High-velocity estimates and inverse scattering for quantum N-body systems with Stark effect
• On multidimensional inverse scattering in an external electric field asymptotically zero in time
• On multidimensional inverse scattering for Stark Hamiltonians
• Inverse scattering problem for time dependent Hartree-Fock equations in the three-body case
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• On the uniqueness of inverse scattering for N-body systems
• Inverse scattering for the nonlinear schrodinger equation
• Low-energy inverse problems in three-body scattering
• The geometrical approach to multidimensional inverse scattering
• Time-dependent methods in inverse scattering problems for the Hartree-Fock equation
• Inverse scattering in the Stark effect
• Inverse scattering of the nonlinear Schrödinger equation with cubic convolution nonlinearity
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