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.
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.
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.
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.
Introduction to the Maths and Physics of Quantum Mechanics details the mathematics and physics that are needed to learn the principles of quantum mechanics. It provides an accessible treatment of how to use quantum mechanics and why it is so successful in explaining natural phenomena. This book clarifies various aspects of quantum physics such as ‘why quantum mechanics equations contain “I”, the imaginary number?’, ‘Is it possible to make a transition from classical mechanics to quantum physics without using postulates?’ and ‘What is the origin of the uncertainty principle?’. A significant proportion of discussion is dedicated to the issue of why the wave function must be complex to properly describe our “real” world. The book also addresses the different formulations of quantum mechanics. A relatively simple introductory treatment is given for the “standard” Heisenberg matrix formulation and Schrodinger wave-function formulation and Feynman path integrals and second quantization are then discussed. This book will appeal to first- and second-year university students in physics, mathematics, engineering and other sciences studying quantum mechanics who will find material and clarifications not easily found in other textbooks. It will also appeal to self-taught readers with a genuine interest in modern physics who are willing to examine the mathematics and physics in a simple but rigorous way. Key Features: Written in an engaging and approachable manner, with fully explained mathematics and physics concepts Suitable as a companion to all introductory quantum mechanics textbooks Accessible to a general audience
This introductory book is aimed at students of engineering and material science who want to learn the necessary toolboxes of practical quantum mechanics. The authors have made sure that all the calculations are complete, and they have avoided the usage of the familiar phrase, “it can be easily shown” while being mathematically rigorous. Knowledge of the sophomore level introduction to ordinary differential equations is all that is needed. Well-designed and modern examples help the reader grasp and digest the concept before moving to the next one. The book offers a lucid exposition to the modern field of quantum computing and quantum gates, two-level systems, orbitals, spin, periodic solids, tunneling, and Fermi golden rule. The basics of electronic and optical properties of nanomaterials using the basics of quantum mechanics are presented without the reader getting lost in research articles with different notations and units. There are numerous examples in the book covering topics such as carbon nanotubes, graphene, superconducting qubits, principle of scanning tunneling microscopy, heterostructure based terahertz generation and negative differential resistance device, quantized LC circuit, Grover’s search algorithm, phase kickback, quantum dots, well, nanowires, quantum of conductance, ballistic conductor, spin-orbit coupling, and spin transistor. Authors use analogies based on familiar engineering concepts wherever possible to broaden the view of the reader. The philosophy behind the book is teaching by showing how it is done and using “pictures” which is worth 1000 words.
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.
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