Abstract The highest level physics course that an engineer is likely to take is Modern Physics, an upper-level class typically offered by the physics department. This course may be required for electrical or computer engineers as a prelude to a semiconductor device class. Surveys of textbooks indicate that the curriculum for such courses has not changed much in a couple of decades. The table of contents of a typical text includes such topics as: relativity, quantization, the Bohr-Rutherford nuclear atom, wave-particle duality and the Heisenberg uncertainty principle, the Schrodinger equation, atomic physics, statistical physics, and various related applications. Virtually none of the popular texts include topics such as quantum entanglement and quantum computing. Quantum entanglement provides correlations in the measurement of physical systems. These systems are usually electrons or photons. In any case, entanglement is the key feature of quantum computing systems and quantum cryptographic information transmission. As such, it is a topic of active current research and development. In our paper we will describe a new method to introduce quantum mechanics, prior to the introduction of the Schrodinger equation. We use the results of recent published research in physics education to introduce students to the concept of simulated quantum computation. No claim is made toward the development of a quantum computer; instead we use a novel technique to simulate its operation. Students are introduced to the concept of a quantum bit or qubit and how the qubits are represented mathematically and how various operators affect them. They use linear algebra and matrix techniques that are familiar to students to develop a novel understanding of that which is quite unfamiliar – quantum mechanics.
Abstract The highest level physics course that an engineer is likely to take is Modern Physics, an upper-level class typically offered by the physics department. This course may be required for electrical or computer engineers as a prelude to a semiconductor device class. Surveys of textbooks indicate that the curriculum for such courses has not changed much in a couple of decades. The table of contents of a typical text includes such topics as: relativity, quantization, the Bohr-Rutherford nuclear atom, wave-particle duality and the Heisenberg uncertainty principle, the Schrodinger equation, atomic physics, statistical physics, and various related applications. Virtually none of the popular texts include topics such as quantum entanglement and quantum computing. Quantum entanglement provides correlations in the measurement of physical systems. These systems are usually electrons or photons. In any case, entanglement is the key feature of quantum computing systems and quantum cryptographic information transmission. As such, it is a topic of active current research and development. In our paper we will describe a new method to introduce quantum mechanics, prior to the introduction of the Schrodinger equation. We use the results of recent published research in physics education to introduce students to the concept of simulated quantum computation. No claim is made toward the development of a quantum computer; instead we use a novel technique to simulate its operation. Students are introduced to the concept of a quantum bit or qubit and how the qubits are represented mathematically and how various operators affect them. They use linear algebra and matrix techniques that are familiar to students to develop a novel understanding of that which is quite unfamiliar – quantum mechanics.
Over the course of the past two to three decades, new tools of presentation and mathematical treatment have emerged and the subject matter of quantum mechanics has gone through significant changes. A Textbook on Modern Quantum Mechanics presents the selected elementary, intermediate, and advance topics with rejuvenated approach to the subject matter. Newly merged topics from contemporary physics and chemistry are included in the text as well as solved examples. The book covers: (i) fundamental discoveries that are the foundation of modern quantum mechanics; (ii) solution of Schrödinger’s wave equation for 1D problems and their importance; (iii) matrix and vector formulation of quantum mechanics; (iv) transformations, symmetries, and conservation laws; (v) angular and spin momenta; (vi) solution of Schrödinger equation for central potentials; (vii) time-independent perturbation theory, variational method and WKB approximation; (viii) quantum theory of scattering; (xi) many-particle systems and their quantum mechanical treatments; (x) time-dependent perturbations and the interaction of fields with matter; (xi) relativistic quantum mechanics; and (xii) quantization of fields and the second quantization. Key Features: It provides everything a student needs to know for succeeding at all levels of the undergraduate and graduate studies. It covers most of the topics that are taught under (a) elementary, (b) intermediate, and (c) advance courses of quantum mechanics at universities and colleges. It has detailed and elegant mathematical treatment with contemporary style of interpretation and presentation in simple English. Solved examples and unsolved exercises that are part of each chapter to consolidate the readers' understanding of fundamental concepts. The subject matter of the book is well tested on the students taught by the author over a period of 30 years. This is a valuable textbook for students pursuing Bachelor of Science, Master of Science, and Doctor of Philosophy (PhD) degrees in the subjects of Physics, Chemistry, and materials science in India, South Asian countries, the United States, and Europe.
This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basis of modern physics research are also included, such as the density matrix, entropy, and measures of entanglement. Written for an undergraduate audience, this book offers a unique and mathematically self-contained treatment of this hugely important topic. Students are guided gently through the text by the author's engaging writing style, with an extensive glossary provided for reference and numerous homework problems to expand and develop key concepts. Online resources for instructors include a fully worked solutions manual and lecture slides.
A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing such topics as Bloch theorem and effective mass theory, crystal orientation effects for zinc-blend and wurtzite Hamiltonian, and quantum entanglements and teleportation. There has been growing interest in the model of semiconductor lasers with non-Markovian relaxation. This book develops a non-Markovian model for the optical gain in semiconductor materials, taking into account the rigorous electronic band-structure and the non-Markovian relaxation using the quantum statistical reduced-density operator formalism. Many-body effects are taken into account within the time-dependent Hartree-Fock equations, and example programs based on Fortran 77 are provided for band-structures of zinc-blend quantum wells. Engineering Quantum Mechanics is intended for advanced undergraduate and graduate students in electrical engineering, physics, and materials science. It also provides the necessary theoretical background for researchers in optoelectronics or semiconductor devices.
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.
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.
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.