This brief and rudimentary chapter on QED has been included to close the circle in the story telling. The aim has been to emphasize the significance of the notion of the planewave in the theory development. With no more than the idea of the planewave and considering the Maxwell equations in free space inside in a cubic box, the Hamiltonian operator for describing the electromagnetic field was obtained. Thereby, the reader was guided to utilize what they already know, while fully respecting the order of operators. A thorough discussion of the QED following the same style of writing which has been pursued in this book would require an independent treatise. Accomplishing such a project would certainly be a noble undertaking. A volume of this kind would also require the inclusion of the theory of special relativity and of a fully-fletched treatment of spin phenomena. The available books on QED, despite being voluminous and comprehensive, are not easily accessible to engineers and technologists. The discussion in this chapter might convince the reader that with reasonable effort the necessary mathematical tools can be developed and satisfactorily understood. The ultimate vision is that the engineers and technologists, once they have acquired a working knowledge of the methods, they will start enriching the quantum field theory by their own unique creative style of thinking. The first five references in the following list provide further detailed information on the structures of the scaffolding matrices in the mathematical physics. The remaining references may assist the reader in digging deeper in QED. The reader can expect to read comprehensive, and at the same time, accessible treatments of the QED, the spin phenomena, and the special theory of relativity in later MQPET Volumes.
This brief and rudimentary chapter on QED has been included to close the circle in the story telling. The aim has been to emphasize the significance of the notion of the planewave in the theory development. With no more than the idea of the planewave and considering the Maxwell equations in free space inside in a cubic box, the Hamiltonian operator for describing the electromagnetic field was obtained. Thereby, the reader was guided to utilize what they already know, while fully respecting the order of operators. A thorough discussion of the QED following the same style of writing which has been pursued in this book would require an independent treatise. Accomplishing such a project would certainly be a noble undertaking. A volume of this kind would also require the inclusion of the theory of special relativity and of a fully-fletched treatment of spin phenomena. The available books on QED, despite being voluminous and comprehensive, are not easily accessible to engineers and technologists. The discussion in this chapter might convince the reader that with reasonable effort the necessary mathematical tools can be developed and satisfactorily understood. The ultimate vision is that the engineers and technologists, once they have acquired a working knowledge of the methods, they will start enriching the quantum field theory by their own unique creative style of thinking. The first five references in the following list provide further detailed information on the structures of the scaffolding matrices in the mathematical physics. The remaining references may assist the reader in digging deeper in QED. The reader can expect to read comprehensive, and at the same time, accessible treatments of the QED, the spin phenomena, and the special theory of relativity in later MQPET Volumes.
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface. The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.
This book attempts to bridge the enormous gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light in one step. Hence, while it is suitable as a reference for the specialist in quantum optics, it also targets the nonspecialists from other disciplines who need to understand light and its uses in research. With a unique approach it introduces a single analytic tool, namely the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross‐disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including laser tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency (EIT), squeezed light, and cavity quantum electrodynamics (QED). A systematic approach is used that starts with the simplest systems – stationary two‐level atoms – then introduces atomic motion, adds more energy levels, and moves on to discuss first‐, second‐, and third‐order coherence effects that are the basis for analyzing new optical phenomena in incompletely characterized systems. Unconventional examples and original problems are used to engage even seasoned researchers in exploring a mathematical methodology with which they can tackle virtually any new problem involving light. An extensive bibliography makes connections with mathematical techniques and subject areas which can extend the benefit of each section to guide readers further. The steady progression from “simple” to “elaborate” makes the book accessible not only to students from traditional subject areas that make use of light (physics, chemistry, electrical engineering, and materials science), but also to researchers from the “hyphenated” subjects of modern science and engineering: the biophysicists using mechanical effects of light, photochemists developing coherent control for rare species detection, biomedical engineers imaging through scattering media, electromechanical engineers working on molecular design of materials for electronics and space, electrical and computer engineers developing schemes for quantum computation, cryptography, frequency references, and so on. To try to identify techniques and ideas that are universal enough to be applied across the bewildering landscape of research on intersecting boundaries of emerging modern disciplines is a great challenge of out time. “Lectures on Light” offers selected insights on quantum dynamics and quantum theory of light for exactly this purpose.
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information