"Theoretical methods in quantum mechanics and optics, with emphasis on semi-classical approximations"

我的研究目的是通过设计新的方法和见解，为理论物理学的发展做出贡献，为当前感兴趣的领域的物理现象提供新的或更好的理解。所使用的工具是数学分析，并酌情辅之以数值计算。我相信，与纯粹的计算方法相比，有一个简单的分析结果提供对物理现象的洞察有明显的优势。 拟议的工作主要涉及一维有限周期系统，例如电子在工程纳米结构中的运动，或者光入射到具有不同(精心选择的)折射率的薄膜上。(这样的工程薄膜装在每个人的口袋里，放在我们的纸币上，作为NRC实验室开发的防伪装置。) 我还将继续开发量子现象的半经典近似。量子力学通常以非常神秘的形式呈现给公众，只适用于原子和其他小粒子。在日常生活中，我们很少意识到量子行为。尽管如此，在日常大小的物体和非常小的物体之间，探索量子行为如何转变为经典行为是有趣的，在日常大小的物体和非常小的物体之间的中等或“介观”区域。我们发展了一个半经典的光学耦合波理论，它有助于理解经典到量子的跃迁。我还建议研究一些旨在模仿量子行为的经典系统。一般来说，它们使用光波，使光的行为方式与量子概率波被认为的作用方式相同。例如，我们利用光波和量子波之间的类比来设计一种“减反射涂层”，它允许电子穿过半导体材料层，而单层材料会反射电子。

The aim of my research is to contribute to the development of theoretical physics by devising new methods and insights that provide new or better understanding of physical phenomena in areas of current interest. The tools used are mathematical analysis supported by numerical calculations as appropriate. I believe that there are clear advantages to have a simple analytic result that provides insight into physical phenomena, over purely computational approaches. The proposed work mostly concerns one-dimensional finite periodic systems, such as electrons moving in engineered nanostructures, or light incident on layers of thin films with different (carefully chosen) refractive indices. (Such engineered thin films are in everybody's pocket, on our paper currency, as an anti-counterfeiting device developed at NRC Labs.) I will also continue developing semi-classical approximations to quantum phenomena. Quantum mechanics is usually presented to the public as very mysterious, applying only to atoms and other small particles. In everyday life we are seldom aware of quantum behaviour. Still, it is interesting to explore the way quantum behaviour goes over to classical behaviour in the intermediate or `mesoscopic' regime between everyday sized things and the very small. We have developed a semi-classical coupled wave theory for optics, which helps to understand the classical to quantum transition. I also propose to work on some classical systems which are designed to mimic quantum behaviour. Generally these use light waves, making light behave in the way that quantum probability waves are believed to act. As an example, we used the analogy between light waves and quantum waves to design an `anti-reflection coating' which allows electrons to pass through layers of semi-conducting material, when a single layer would reflect them..