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，因此是许多化学和物理学的基础。 在过去的几十年里，人们付出了巨大的努力来近似其解，但高质量的数值解被证明是难以捉摸的。 最近开发的用于高维计算的数学工具揭示了一条通往这种解决方案的新途径，本项目将探索这一途径。 这些解决方案将能够精确计算分子和材料的化学和物理性质，从而对化学、物理学、生物学和材料科学中的许多问题产生影响。这项研究将在俄亥俄州大学数学系进行，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，并将重新致力于加强各级研究。 该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，并在计算数学方面发展有价值的技能。 学生们还将了解研究过程，并发展他们的数学交流技能。

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.