Numerical methods in quantum dynamics

量子动力学中的数值方法

• 批准号: 79255480
• 负责人: Professor Dr. Christian Lubich
• 金额: --
• 依托单位: Arbeitsbereich Numerische Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2008
• 资助国家: 德国
• 起止时间: 2007-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/79255480?language=en
• 关键词: Numerical; methods; quantum; dynamics

The project deals with numerical methods for molecular quantum dynamics, both in devising new methods and in the mathematical analysis of known and novel methods. The numerical difficulties lie in the high dimensionality of the underlying Schrödinger equation as the basic model equation as wellas in the treatment of high oscillations and multiple scales. The project focuses on time-dependent aspects, complementing approaches to the stationary Schrödinger eigenvalue problem within the Priority Research Programme. The research will concentrate on dynamical low-rank approximations such as the time-dependent multi-configuration Hartree and Hartree-Fock methods on the one hand, and on a novel computational approach to the time-dependent Schrödinger equation in semi-classical scaling (for nuclei in a molecule) based on Hagedorn wavepackets.

该项目涉及分子量子动力学的数值方法，包括设计新方法以及对已知和新方法的数学分析。数值计算的困难在于作为基本模型方程的薛定谔方程的高维性以及高振荡和多尺度的处理。该项目的重点是时间依赖方面，补充方法的固定薛定谔本征值问题内的优先研究计划。这项研究将集中在动力学低秩近似，如含时多组态Hartree和Hartree-Fock方法，一方面，在一个新的计算方法的含时薛定谔方程的半经典标度（在一个分子中的核）的基础上哈格多恩波包。