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

“量子力学和光学的理论方法，重点是半经典近似”

• 批准号: 3198-2012
• 负责人: Sprung, Donald
• 金额: $ 1.24万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568279
• 关键词: Theoretical; methods; quantum; mechanics; optics

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..

我的研究目的是通过设计新的方法和见解，为当前感兴趣的领域的物理现象提供新的或更好的理解，从而为理论物理学的发展做出贡献。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，与纯粹的计算方法相比，简单的分析结果有明显的优势，可以提供对物理现象的洞察。