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

我的研究的目的是通过设计新的方法和见解，提供新的或更好地理解当前感兴趣的领域的物理现象，为理论物理的发展做出贡献。 所使用的工具是由适当的数值计算支持的数学分析。我相信，有一个简单的分析结果，提供了对物理现象的洞察力，在纯粹的计算方法有明显的优势。 拟议的工作主要涉及一维有限周期性系统，如电子在工程纳米结构中移动，或入射到具有不同（精心选择的）折射率的薄膜层上的光。 (Such每个人的口袋里都有工程薄膜，在我们的纸币上，作为NRC实验室开发的防伪设备。 我也将继续发展量子现象的半经典近似。量子力学在公众面前通常是非常神秘的，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。不过，在介于日常大小的物体和非常小的物体之间的中间或“介观”状态下，探索量子行为如何过渡到经典行为是很有趣的。我们发展了一个半经典耦合波理论，它有助于理解经典到量子的转变。我还建议研究一些经典系统，这些系统被设计成模仿量子行为。一般来说，它们使用光波，使光以量子概率波被认为的方式行为。作为一个例子，我们使用光波和量子波之间的类比来设计一种“抗反射涂层”，它允许电子通过半导体材料层，而单层材料会反射它们。

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..