Continuing size reduction in mesoscopic and nanoscopic electronic, photonic, and plasmonic devices makes the employment of quantum physics (QP) and quantum electrodynamics (QED) inevitable. Engineers at the forefront of these fields increasingly need to have a working knowledge of QP and, more importantly, feel confident to manoeuver through the intricate calculations involved. However, electrical engineers and applied physicists are typically unfamiliar with the sophisticated mathematical apparatus in QP and QED, which is generally perceived to be formidably abstract. The Mathematical Quantum Physics for Engineers and Technologists volumes aim to explain the mathematical foundation of QP and QED to engineers using an engineer's mindset as the starting point, and following a new line of thinking based on clarity and obviousness. Written for an audience of researchers and advanced students in electrical engineering, computer science, applied mathematics and applied physics, the Mathematical Quantum Physics for Engineers and Technologists volumes guide readers towards acquiring a solid understanding of the mathematical intricacies of quantum physics and quantum electrodynamics. Volume 1 covers topics including the resolution of identity, generalized functions, bases, dual bases, frames, dual frames, generalized transforms and inverse transforms, operator gymnastics, canonical commutation relationships, standard and generalized creation and annihilation operators.
Continuing size reduction in mesoscopic and nanoscopic electronic, photonic, and plasmonic devices makes the employment of quantum physics (QP) and quantum electrodynamics (QED) inevitable. Engineers at the forefront of these fields increasingly need to have a working knowledge of QP and, more importantly, feel confident to manoeuver through the intricate calculations involved. However, electrical engineers and applied physicists are typically unfamiliar with the sophisticated mathematical apparatus in QP and QED, which is generally perceived to be formidably abstract. The Mathematical Quantum Physics for Engineers and Technologists volumes aim to explain the mathematical foundation of QP and QED to engineers using an engineer's mindset as the starting point, and following a new line of thinking based on clarity and obviousness. Written for an audience of researchers and advanced students in electrical engineering, computer science, applied mathematics and applied physics, the Mathematical Quantum Physics for Engineers and Technologists volumes guide readers towards acquiring a solid understanding of the mathematical intricacies of quantum physics and quantum electrodynamics. Volume 1 covers topics including the resolution of identity, generalized functions, bases, dual bases, frames, dual frames, generalized transforms and inverse transforms, operator gymnastics, canonical commutation relationships, standard and generalized creation and annihilation operators.
Continuing size reduction in mesoscopic and nanoscopic electronic, photonic, and plasmonic devices makes the employment of quantum physics (QP) and quantum electrodynamics (QED) inevitable. Engineers at the forefront of these fields increasingly need to have a working knowledge of QP and, more importantly, feel confident to manoeuver through the intricate calculations involved. However, electrical engineers and applied physicists are typically unfamiliar with the sophisticated mathematical apparatus in QP and QED, which is generally perceived to be formidably abstract. The Mathematical Quantum Physics for Engineers and Technologists volumes aim to explain the mathematical foundation of QP and QED to engineers using an engineer's mindset as the starting point, and following a new line of thinking based on clarity and obviousness. Written for an audience of researchers and advanced students in electrical engineering, computer science, applied mathematics and applied physics, the Mathematical Quantum Physics for Engineers and Technologists volumes guide readers towards acquiring a solid understanding of the mathematical intricacies of quantum physics and quantum electrodynamics. Volume 2 covers topics including the ideal and perturbed quantum harmonic oscillator, the displacement operator, squeezed states, single electron systems, the Schrödinder picture, the Heisenberg picture, the Interaction picture, the Feynman path integral, the standard and generalized Trotter product formula, and quantum electrodynamics.
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results.Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.
Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Third Edition provides a complete course in quantum mechanics for students of semiconductor device physics and electrical engineering. It provides the necessary background to quantum theory for those starting work on micro- and nanoelectronic structures and is particularly useful for those beginning work with modern semiconductors devices, lasers, and qubits. This book was developed from a course the author has taught for many years with a style and order of presentation of material specifically designed for this audience. It introduces the main concepts of quantum mechanics which are important in everyday solid-state physics and electronics. Each topic includes examples which have been carefully chosen to draw upon relevant experimental research. It also includes problems with solutions to test understanding of theory. Full updated throughout, the third edition contains the latest developments, experiments, and device concepts, in addition to three fully revised chapters on operators and expectations and spin angular momentum, it contains completely new material on superconducting devices and approaches to quantum computing.
This book presents a comprehensive treatment of quantum theory using theoretical variables as its foundation. The work progresses from fundamental quantum mechanical principles to sophisticated applications in quantum field theory and gravity. It provides rigorous mathematical frameworks while establishing connections between theoretical physics and practical engineering applications. Particularly suitable for graduate students and researchers in physics, mathematics, and engineering disciplines seeking to understand quantum phenomena across theoretical and applied domains. Presents an advanced treatment of quantum theory across two interconnected parts Examines Bell experiments, quantum probability, information theory, and connections to relativity Extends these foundations to explore quantum field theory, gravity, and noise theory Bridges the gap between theoretical physics and engineering applications Covers topics from Yang-Mills fields, quantum gravity to neural networks and biomedical applications of quantum electrodynamics Addresses quantum measurement of gravitons, Hawking radiation, classical and quantum neural networks with practical examples Provides mathematical frameworks for understanding quantum phenomena in applied contexts This title has been co-published with Manakin Press. Taylor & Francis does not sell or distribute the print edition in India, Pakistan, Nepal, Bhutan, Sri Lanka and Bangladesh.
Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Fourth Edition provides a complete course in quantum mechanics for students of semiconductor device physics and electrical engineering. It provides the necessary background to quantum theory for those starting work on micro- and nanoelectronic structures and is particularly useful for those beginning work with modern semiconductors devices, lasers and qubits. This book was developed from a course the author has taught for many years with a style and order of presentation of material specifically designed for this audience. It introduces the main concepts of quantum mechanics which are important in everyday solid-state physics and electronics. Each topic includes examples which have been carefully chosen to draw upon relevant experimental research. It also includes problems with solutions to test understanding of theory. Fully updated throughout, the fourth edition contains the latest developments, experiments, and device concepts. It contains completely new material on quantum computing and information processing, including qubit implementations and quantum sensing. Key features: Fully updated throughout with the latest research from the field Presents a different view of quantum mechanics from an engineering perspective Takes a modern view of the understanding of quantum mechanics as it affects real world technologies, including nanotechnology and quantum information processing
Notes on Theoretical Physics offers a detailed exposition of fundamental areas within theoretical physics and its mathematical foundations. The primary objective of this work is to present explicit, step-by-step mathematical developments, intentionally avoiding the systemic use of natural units or excessive simplifications that can otherwise obscure dimensional analysis and the tracking of fundamental constants. By preserving the explicit identity of algebraic operations and differential representations, the text aims to maintain transparency in the interplay between mathematical formalism and physical interpretation. The scope includes topics ranging from classical analytical mechanics and electrodynamics to advanced mathematical tools, such as the treatment of distribution theory within the framework of topological dual spaces. Conceived as an open and evolving pedagogical project, this work is intended to serve as a reference for students and researchers seeking foundational depth. Given the breadth of the subjects covered, the author remains fully aware that errata and areas for improvement are inevitable. Therefore, the scientific and student community is warmly invited to engage in a critical reading; any formal corrections or suggestions will be integrated into future revisions, with due acknowledgment of contributors in subsequent editions.