Some Aspects of Quantum Theory
SOME ASPECTS OF QUANTUM THEORY John Scales Avery August 22, 2020 INTRODUCTION1 I hope that this book will be of interest to students and researchers in mathematics, physics and theoretical chemistry. The first few chapters can be read with ease by anyone with a knowledge of calculus and differential equations. However, some later chapters, and most of the appendices, are more demanding.. Chapter 10 deals with resonance energy transfer and especially with the relativistic treatment of this phenomenon. My fascination with this topic dates back to my Ph.D. thesis work in the early 1960’s at Imperial College, which was then a part of the University of London. I had previously been working at the laboratory of Prof. Albert Szent-Gy¨orgyiand the Marine Bi- ological Laboratory at Woods Hole, Massachusetts. The problem on which we had been working was a quantum mechanical treatment of the primary process in photosynthesis, where a photon is absorbed, and its energy stabi- lized. Resonance energy transfer plays a large role in this process2. When I started my Ph.D. work in London, I decided to see whether relativistic corrections made a difference3. My calculations4 showed that while the usual non-relativistic treatment leads to transition probabilities that fall off as 1/R6, the calculated relativistic transition probabilities had a long-range component that fell off as 1/R2. Thus,if we imagine a very large sphere around an excited atom of molecule, the probability that the excitation energy will be transferred to one or another of the acceptors is independent of the size of the sphere! Is this a process that competes with spontaneous photon emission? Or is it an alternative way of treating the joint process of emission and absorption?5 Today, sixty years later, I continue to be fascinated by this question.
[Show full text]