Mathematical Sciences: Mathematical Studies in Quantum Mechanics

这项研究的主要目标将是研究分子系统。使用Born-Oppenheimer近似研究电子能级交叉、(无限时间)散射问题以及涉及振荡外部电场的问题的早期工作将得到扩展。数值计算将被用来检验高阶Born-Oppenheimer展开式在现实系统中的有效性。还将研究一类特殊的一维薛定谔算子。这项研究将对准晶的研究产生影响。

The primary goal of this research will be to study molecular systems. Earlier work which used the Born-Oppenheimer approximation to study electron energy level crossings, (infinite time) scattering problems, and problems that involve oscillating external electric fields will be extended. Numerical calculations will be used to test the usefulness of high order Born-Oppenheimer expansions on realistic systems. Also studied will be a particular family of one-dimensional Schrodinger operators. This research should have impact on the study of quasicrystals.