This graduate text introduces relativistic quantum theory, emphasising its important applications in condensed matter physics. Basic theory, including special relativity, angular momentum and particles of spin zero are first reprised. The text then goes on to discuss the Dirac equation, symmetries and operators, and free particles. Physical consequences of solutions including hole theory and Klein's paradox are considered. Several model problems are solved. Important applications of quantum theory to condensed matter physics then follow. Relevant theory for the one electron atom is explored. The theory is then developed to describe the quantum mechanics of many electron systems, including Hartree-Fock and density functional methods. Scattering theory, band structures, magneto-optical effects and superconductivity are among other significant topics discussed. Many exercises and an extensive reference list are included. This clear account of relativistic quantum theory will be valuable to graduate students and researchers working in condensed matter physics and quantum physics.
This graduate text introduces relativistic quantum theory, emphasising its important applications in condensed matter physics. Basic theory, including special relativity, angular momentum and particles of spin zero are first reprised. The text then goes on to discuss the Dirac equation, symmetries and operators, and free particles. Physical consequences of solutions including hole theory and Klein's paradox are considered. Several model problems are solved. Important applications of quantum theory to condensed matter physics then follow. Relevant theory for the one electron atom is explored. The theory is then developed to describe the quantum mechanics of many electron systems, including Hartree-Fock and density functional methods. Scattering theory, band structures, magneto-optical effects and superconductivity are among other significant topics discussed. Many exercises and an extensive reference list are included. This clear account of relativistic quantum theory will be valuable to graduate students and researchers working in condensed matter physics and quantum physics.
This graduate text introduces relativistic quantum theory, emphasising its important applications in condensed matter physics. Basic theory, including special relativity, angular momentum and particles of spin zero are first reprised. The text then goes on to discuss the Dirac equation, symmetries and operators, and free particles. Physical consequences of solutions including hole theory and Klein's paradox are considered. Several model problems are solved. Important applications of quantum theory to condensed matter physics then follow. Relevant theory for the one electron atom is explored. The theory is then developed to describe the quantum mechanics of many electron systems, including Hartree-Fock and density functional methods. Scattering theory, band structures, magneto-optical effects and superconductivity are among other significant topics discussed. Many exercises and an extensive reference list are included. This clear account of relativistic quantum theory will be valuable to graduate students and researchers working in condensed matter physics and quantum physics.
Over the past few decades, in concert with ground-breaking experimental advances, condensed matter theory has drawn increasingly from the language of low-energy quantum field theory. This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. It emphasizes the development of modern methods of classical and quantum field theory with applications oriented around condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked solutions, designed to provide a bridge between formal manipulations and research-oriented thinking. This book will complement graduate level courses on theoretical quantum condensed matter physics.
Modern Quantum Mechanics and Quantum Information surveys the fundamental aspects of quantum mechanics against the backdrop of its use in modern science applications. The book covers several topics in modern quantum mechanics and quantum information that do not appear in older texts. These include a mathematically sound treatment of delta functions and the rigged Hilbert space, an exposition of many-body theory including density functional theory and Feynman diagrams, and an explanation of chemical bonds and energy band theory. It also contains expansive chapters on relativistic Dirac theory, group theory including Lie groups, exotic quantum phenomena, interpretations of quantum theory, quantum computers and quantum cryptography. Each chapter ends with a set of questions and exercises for the student. This authoritative and expansive survey of the field is ideal for advanced researchers, upper undergraduate and graduate studentss, with a main purpose as a text for a graduate course in quantum mechanics. Key features • Provides a thorough review of the basics • Discusses the philosophical questions of quantum theory • Includes the concepts used in quantum condensed matter physics and quantum chemistry in detail • Presents quantum information • Discusses the density functional and the diagrammatic approaches to many-body theory
Quantum Mechanics will enthuse graduate students and researchers and equip them with effective methodologies for challenging applications in atomic, molecular, and optical sciences and in condensed matter and nuclear physics also. This book attempts to make fundamental principles intuitively appealing. It will assist readers in learning difficult methods. Exposition of fundamental principles includes a discussion on position-momentum and energy-time uncertainty, angular momentum algebra, parity, bound and unbound eigenstates of an atom, approximation methods, time-reversal symmetry in collisions, and on a measurable time delay in scattering. It also provides an early introduction to Feynman path integrals and to geometric phase. A novel Lambert-W method to solve quantum mechanical problems is also introduced. It seeks to enable readers gain confidence in applying methods of non-relativistic and relativistic quantum theory rigorously to problems on atomic structure and dynamics, spectroscopy and quantum collisions, and problems on introductory quantum information processing and computing.
Chapter 19 introduces relativistic quantum mechanics, with the aim of providing the student with a basic knowledge of the subject and a link to more advanced courses in relativistic quantum theory. It begins by showing that when the Schrödinger equation is modified to make it consistent with special relativity, the result is the Klein–Gordon equation, which gives better qualitative agreement with experiment. Introducing the electron spin into the Schrödinger equation leads to the Pauli equation, which gives rise to important spin effects. By considering both special relativity and spin, one obtains the Dirac and the van der Waerden equations. The main properties and implications of Dirac’s equation are discussed, including the electron’s zitterbewegung. The solution of Dirac’s equation for the free particle is presented in detail, the hydrogen-like atom is shown to be exactly solvable, and the particle in an external electromagnetic field is included as a complementary material.
Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.