CAREER: Toward Direct Numerical Solution of the Multiparticle Schrodinger Equation

多粒子薛定谔方程是量子力学中的基本控制方程，因此也是许多化学和物理的基础。几十年来，人们花了大量的精力来近似它的解，但事实证明，高质量的数值解是难以捉摸的。最近开发的用于高维计算的数学工具揭示了一条通向此类解决方案的新途径，本项目将探索这一途径。这些解决方案将使分子和材料的化学和物理性质得到准确的计算，从而对化学、物理、生物学和材料科学的许多问题产生影响。这项研究将在俄亥俄大学数学系进行，这是一所位于俄亥俄州东南部阿巴拉契亚地区的州立大学，它将重新承诺加强各级研究。研究小组将包括本科生和研究生，他们将为这个项目做出贡献，并发展计算数学方面的宝贵技能。学生还将了解研究过程，并培养他们交流数学的技能。

The multiparticle Schrodinger equation is the basic governing equation in quantum mechanics, and thus the foundation for much of chemistry and physics. A tremendous amount of effort, over several decades, has gone into approximating its solutions, but high-quality numerical solutions have proved elusive. Recently-developed mathematical tools for computing in high dimensions have revealed a new path toward such solutions, which this project will explore. Such solutions will enable accurate computation of chemical and physical properties of molecules and materials, and thus have an impact on many problems in chemistry, physics, biology, and materials science.This research will occur in the Department of Mathematics at Ohio University, a state university located in the Appalachian region of southeastern Ohio, with a renewed commitment to strengthening its research at all levels. The research group will include both undergraduate and graduate students, who will contribute to this project and develop valuable skills in computational mathematics. The students will also learn about the research process and develop their skills at communicating mathematics.