This paper is devoted to the exposition of operator algebraic methods that can be usefully applied to many areas of physical optics. These methods exploit the structural similarity between physical optics and quantum mechanics and make use of operator techniques widely used in quantum theory. We develop the basic approach here and illustrate its power by giving a compact derivation of the Fourier properties and the imaging properties of an ideal lens. We also use the operator approach to introduce and discuss operators and fields that are unaltered by passage through an optical system.
This paper is devoted to the exposition of operator algebraic methods that can be usefully applied to many areas of physical optics. These methods exploit the structural similarity between physical optics and quantum mechanics and make use of operator techniques widely used in quantum theory. We develop the basic approach here and illustrate its power by giving a compact derivation of the Fourier properties and the imaging properties of an ideal lens. We also use the operator approach to introduce and discuss operators and fields that are unaltered by passage through an optical system.
The field of quantum optics has witnessed significant theoretical and experimental developments in recent years. This book provides an in-depth and wide-ranging introduction to the subject, emphasising throughout the basic principles and their applications. The book begins by developing the basic tools of quantum optics, and goes on to show the application of these tools in a variety of quantum optical systems, including lasing without inversion, squeezed states and atom optics. The final four chapters are devoted to a discussion of quantum optical tests of the foundations of quantum mechanics, and to particular aspects of measurement theory. Assuming only a background of standard quantum mechanics and electromagnetic theory, and containing many problems and references, this book will be invaluable to graduate students of quantum optics, as well as to researchers in this field.
This is the third edition of a successful and well-established text. Thoroughly revised and updated, the book provides a comprehensive introduction to the fundamentals of optics, and to a wide variety of more advanced areas of modern optical science. Several new sections have been added, including discussions of super-resolved imaging, phase-retrieval in optical and X-ray diffraction, phase-conjugate imaging and squeezed-light interferometry. Throughout, the subject matter is developed by a combination of unsophisticated mathematics and physical intuition, with particular emphasis being placed on Fourier analysis. The very broad range of subjects treated, together with the inclusion of many problems and over 300 diagrams and photographs, will make the book of great use to undergraduate and graduate students of physics, and to anyone working in the field of optical science.
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related to the Yang-Baxter equations. Physical meaning of abstract mathematical notions like universal R-matrix, quantized algebras, Sklyanin algebra, braided algebra, Hopf algebra etc. and the role played by them in integrable systems are highlighted. Systematic construction of quantum integrable lattice as well as field models and their exact excitation spectra are presented through examples. The coordinate and algebraic formulations of the Bethe ansatz are illustrated with comparison, along with the description of nested and functional Bethe ansatzes. The techniques for deriving quantum Hamiltonians from the Lax operators are demonstrated on concrete models. The exposition of this review is kept in a fairly elementary level with emphasis on the physical contents.
We often hear at seminars and presentations ‘Show me the Hamiltonian of your problem and I will tell you what problem you are talking about’. Therefore, to understand what quantum optics is about, we start from the description of a standard Hamiltonian of the problems considered in quantum optics. We illustrate the method of derivation of the explicit form of the Hamiltonian for a simple system that is composed of two subsystems that interact (communicate) with each other. As we shall see, the explicit form of the Hamiltonian is essential to explicitly calculate energy levels of a given combined system and the temporal evolution of an arbitrary operator representing the system.
This paper has to do with the introduction of an algebraic operator method suitable for applications in a wide area of optics. The algebraic structure of this method allows us to derive results usually obtained by using the method of rays in classical optics. Here, we treat the propagation of electromagnetic waves in the framework of paraxial approach, where the paraxial wave equation is viewed as the Schrödinger's wave equation of quantum theory. The time variable of the Schrödinger's equation plays the role of a coordinate along the propagation axis. From this point of view, a formal analogy among the wave optics and quantum mechanics is constructed. In this work, the impulse response function (IRF) for a thick lens is obtained, and from this, the well known corresponding matrix transformation in classical optics is deduced.
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses recent emergence of the unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis, with potentially significant physical consequences. In addition to prompting a discussion of the role of mathematical methods in the contemporary development of quantum physics, the book features: * Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area * An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and pertubation theory * Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics, condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.