Time-dependent methods in inverse scattering problems for the Hartree-Fock equation
| Autor: | Michiyuki Watanabe |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
Scattering Nuclear Theory 010102 general mathematics Hartree–Fock method FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) 01 natural sciences Schrödinger equation symbols.namesake Mathematics - Analysis of PDEs Uniqueness theorem for Poisson's equation 0103 physical sciences Inverse scattering problem Scattering operator symbols FOS: Mathematics 010307 mathematical physics Limit (mathematics) 0101 mathematics Reconstruction procedure Mathematical Physics Mathematical physics Analysis of PDEs (math.AP) |
| Popis: | The inverse scattering theory for many-body systems in quantum mechanics is an important and difficult issue not only in physics---atomic physics, molecular physics and nuclear physics---but also mathematics. The major purpose in this paper is to establish a reconstruction procedure of two-body interactions from scattering solutions for a Hartree-Fock equation. More precisely, this paper gives a uniqueness theorem and proposes a new reconstruction procedure of the short-range and two-body interactions from a high-velocity limit of the scattering operator for the Hartree-Fock equation. Moreover, it will be found that the high-velocity limit of the scattering operator is equal to a small-amplitude limit of it. The main ingredients of mathematical analysis in this paper are based on the theory of integral equations of the first kind and a Strichartz type estimates on a solution to the free Schr\"{o}dinger equation. |
| Databáze: | OpenAIRE |
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