Mathematical Sciences: The Schrodinger Equation

赫布斯特将在量子力学的偏微分方程组领域进行研究。要考虑的问题涉及散射理论和描述束缚粒子的薛定谔方程解的渐近行为。前一项工作将涉及本征函数展开、对角化N粒子哈密顿量以及零次齐次势的散射理论的研究。现代物理学，量子力学和相对论，是二十世纪的产物。它是在上个世纪试图解决物质的微观结构并掌握远距离作用力、电磁学和热辐射等概念的过程中建立起来的。这些发展的数学基础统称为数学物理，从控制粒子动力学的薛定谔算符的详细分析，到试图将四种已知力统一为单一理论的统一场论。

Herbst will conduct research in the area of partial differential equations in quantum mechanics. The problems to be considered concern scattering theory and the asymptotic behavior of solutions to the Schrodinger equation which describe bound particles. The former work will involve eigenfunction expansions diagonalizing N-particle Hamiltonians and the investigation of the scattering theory of homogeneous potentials of degree zero. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.