Mathematical Sciences: Singular Perturbations, Oscillatory Integrals, and Point Interactions

Hughes教授将把Ricci和Stein关于振荡积分的工作应用于量子力学中出现的奇异摄动问题。此外，休斯将考虑具有奇异时变相互作用的时变薛定谔方程的解。一个统一的主题将是对薛定谔方程解的相互作用表示的使用。这项工作涉及到量子力学的数学。休斯教授将运用新的数学技术来理解相互作用的量子力学粒子的行为。

Professor Hughes will apply work of Ricci and Stein on oscillatory integrals to singular perturbation problems arising in quantum mechanics. In addition Hughes will consider the solution of the time dependent Schroedinger equation with singular time dependent interactions. A unifying theme will be the use of the interaction representation for solutions of the Schroedinger equation. This work involves the mathematics of quantum mechanics. Professor Hughes will apply new mathematical techniques to understand the behavior of interacting quantum mechanical particles.