Computability of magnetic Schrodinger and Hartree equations on unbounded domains

被引：0

作者：

Becker, Simon ^{[1
]}

Sewell, Jonathan ^{[2
]}

Tebbutt, Euan ^{[3
]}

机构：

[1] Swiss Fed Inst Technol, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Univ Bath, Dept Math Sci, Bath, Avon, England

[3] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 02期

关键词：

Hartree equation; Schrodinger equation; unbounded domains; WIGNER-POISSON; UNIQUENESS; EXISTENCE;

D O I：

10.1002/num.22935

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the computability of global solutions to linear Schrodinger equations with magnetic fields and the Hartree equation on Double-struck capital R-3. We show that the solution can always be globally computed with error control on the entire space if there exist a priori decay estimates in generalized Sobolev norms on the initial state. Using weighted Sobolev norm estimates, we show that the solution can be computed with uniform computational runtime with respect to initial states and potentials. We finally study applications in optimal control theory and provide numerical examples.

引用

页码：1299 / 1332

页数：34

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