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

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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..