A basic level Quantum Mechanics book for beginners in UG & PG Physics. In fact Quantum Mechanics is not Mathematics. But many teachers even now treating this subject as Mathematics. It has its own concepts and ideas. Without this understanding one cannot excel in Quantum Mechanics. Inadequacy of classical physics led to Quantum Mechanics and it was able to prove the mechanics in microlevel. Mathematics can be used as a language for understanding. After estimating wave function, the physics behind it has to be understood. For this authors tried to avoid mathematical steps. But included all necessary steps. This book is highly helpful for students to understand the basics of Quantum Mechanics.
This publication is about quantum mechanics and about real phenomena hidden by the formalism of quantum mechanics. Quantum mechanics assumes the existence of quantum waves and superposition states. However, the existence of these cannot be experimentally demonstrated. A new way to explain formation of the interference fringes created by particles without assuming the existence of quantum waves is used to reveal the origin of Bohr’s philosophy and the Copenhagen interpretation of quantum mechanics. This new approach is also used to show that EPR, delayed choice, quantum eraser and which-way experiments do not test quantum mechanics adequately. The presented text gives an approach how to look at quantum mechanics and see beyond its formalism. This gives ideas for new tests. The publication is directed to researchers interested in fundamentals of quantum mechanics but also to all physicists who can appreciate mystery and strangeness of this theory.
Quantum Mechanics is a nondeterministic theory that its mathematical predictions coincide with physical measurements and observations and studies the fundamental questions underlying modern physics a bout time, space,energy and matter and its answeres has philosophical interpretations.Modern Quantum Mechanics is aimed at first - year graduate students begins with the mathematical tools of Quantum Mechanics and its representations, The next chapter is about Sherodinger equation,Heisenberg picture, Propagators and Guage transformations and the last chapter deals with Angular momentum,Rotation Groups,Bells Inequality, Ensembles and Density Operators.
Quantum mechanics allows accurate predictions of nature, yet it also uncovers surprises like teleportation and multiple universes. It involves complicated mathematics, yet most general reader texts avoid mathematics. This book uses on high-school level mathematics to provide a deeper understanding of quantum mechanics.
Quantum particles are the main theme ideas of quantum mechanics. We cannot imagine the matter of quantum mechanics without considering these microparticles and their motion. According to German Physic’s Max Planck, classical mechanics fails to study the motion of micro particle like electron then new modern physics named Quantum Mechanics grows at the end of nineteen century and Planck expressed it in Einstein’s hypothesis of light quanta. This book demonstrates the motion of quantum particle like electron with the help of some Mathematical form of Schrodinger wave equation. Here we use The Variational iterative method which reduces the size of calculations. This method provides a well-organized and much effective method for handling this nonlinear behaviour.
Quantum field theories are quite difficult. The successes achieved by using quantum field theories are rather limited because in these theories one faces various difficulties. Later Dirac introduced an alternative process to quantize the fields. He introduced Hamiltonian equations of motion from Lagrangian to describe the laws of mechanics and gravitation. It has wide application in classical mechanics, quantum mechanics and quantum field theory, as well as in general relativity etc. One may deal with Hamiltonian in general frameworks as well as oscillatory systems.
The book is negotiating the problem of the hidden variables in quantum mechanics. "People who have read quantum mechanics and have not been shocked have not understood it" as has been said by one of the founders of this theory. Everything in nature must happen for a reason according to the author. It is also a good practice to give one the tools with which he can make his own research or complete upon the writings. These are the basic ideas of this book
This book presents a complete review of the theory of nonlinear quantum mechanics and which differs totally from the original discipline of quantum mechanics as well as the studies the nature of microscopic particles under action of the nonlinear interactions in the systems; which give numerous new and interesting properties and rules of motions of the particles, such as wave-corpuscle duality and localization, and which discusses the applications of theory as relates to condensed matter, polymers, and biological systems. It is intended for researchers, teachers, graduate students and upper-level undergraduate students. The so-called discipline of nonlinear quantum mechanics (NLQM) is, in reality, only a theory for studying the properties and motion of microscopic particles (MIPs) in nonlinear physical systems. It was so named in relation to the concept of quantum mechanics established by Bohr, Heisenberg, Schrodinger and numerous others. The latter deals only with the properties and motion of microscopic particles in linear systems without nonlinear interactionh and will, here-in-after, referred to as linear quantum mechanics (LQM). The following topics are covered in 6 chapters i
The main topic of this book is quantum mechanics, as the title indicates. It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory. It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions. Two key features make this book different from others on quantum mechanics, even those usually intended for engineers: First, after a brief introduction, much of the development is through Fourier theory, a topic that is at the heart of most electrical engineering theory. In this manner, the explanation of the quantum mechanics is rooted in the mathematics familiar to every electrical engineer. Secondly, beginning with the first chapter, simple computer programs in MATLAB are used to illustrate the principles. The programs can easily be copied and used by the reader to do the exercises at the end of the chapters or to just become more familiar with the material. Many of the figures in this book have a title across the top. This title is the name of the MATLAB program that was used to generate that figure. These programs are available to the reader. Appendix D lists all the programs, and they are also downloadable at http://booksupport.wiley.com
The present book contains one hundred and sixty problems, most of them simple, in nonrelativistic quantum mechanics. Some of these problems were used previously by the authors in their courses at the Moscow Institute of Engineering and Physics. However, the majority were drawn up or selected in the course of work on the book. This book is designed for physics students who are studying quantum mechanics approximately at the level of D.I.Blokhintsev's book or Part II of "Theoretical Physics" by A.S.Kompaneyts. A number of problems is intended primarily for students who are beginning to specialize in theoretical physics and who are partially familiar with the contents of "Quantum Mechanics" by L.D.Landau and Ye.M.Lifshits. Some problems illustrate individual theoretical questions which have scarcely been considered in textbooks: sudden and adiabatic changes; Heisenberg representation of operators; probability relations in addition of momenta; isotopic spin; parity; and others. The authors have tried to use relatively elementary mathematical tools of quantum mechanics to facilitate use of the book by nontheoretical physicists. With a few exceptions, the authors have not included in this book problems which are considered in sufficient detail in the basic textbooks mentioned above and in the problem book on quantum mechanics written by V.G.Levich. Therefore, this book should be regarded chiefly as an auxiliary textbook in the study of the above books.
Written by physicist and broadcaster Professor Jim Al-Khalili, it explores all the key players, breakthroughs, controversies and unanswered questions of the quantum world.You'll discover how the sun shines, why light is both a wave and a particle, the certainty of the Uncertainty Principle, Schrodinger's Cat, Einstein's spooky action, how to build a quantum computer, and why quantum mechanics drives even its experts completely crazy.
The weird quantum mechanical effects governing the behavior of sub-atomic particles are about to revolutionize the way we perform computation and manipulate information. This book is a testimony to the indelible mark that quantum mechanics has already left on computer science. Specifically, we have investigated some of the consequences of manipulating information at the quantum level on data security, parallel processing, universality and computability.
In this work we study two non-classical features of quantum compound systems, namely, entanglement and indistinguishability using logical and algebraic techniques. First, we study improper mixtures from a quantum logical and geometrical point of view. This is done by extending the von Neumann lattice of propositions in order to include improper mixtures as atoms of the new lattice. Then, we study the problem of quantum non-individuality. We use a quantum structure which is a modification of Zermelo-Frenkel set-theory based on quantum mechanics, namely, Quasi-set Theory (Q). Using Q we develop a new formulation of quantum mechanics which does not uses first order identity on its logical bases. These constructions answer interesting discussions posed in the literature.
This book is destined for scientific workers and professors in the field of quantum mechanics and quantum theory of collisions, students and post-graduate students and all interested in quantum mechanics, quantum field theory and nuclear physics. The book contains the chapter of fundamental quantum mechanics and quantum field theory – on time as a quantum observable for systems with continuous and discrete spectra. In its completed form this book could not be written up to now due to a number of the mathematical problems. Some mathematicians had been known the solution of these problems in the field of operator theory in Hilbert spaces for systems with continuous energy spectrum. But practically these problems were unknown for almost of all physicists, with the exception of the author and his friend. Overcoming these and other mathematical problems permitted finally to develop and apply the methods of time analysis of quantum processes and write this book. Moreover, in it there are exposed also many applications of time analysis of quantum processes and paradoxes for tunneling and collisions (nuclear reactions)which were elaborated by author, partly together with colleagues.
The book contains the developments in quantum mechanics as well as the basic concepts of quantum formalism in simple terms. Quantum Mechanics is the science of motion of atomic and sub atomic Particles. Experimental measurements for atomic and molecular systems shows that an electron moving around the nucleus of an atom has only a discrete set of values of energy. Rotational motion of particle is of great interest in atomic and molecular problems. For single particle executing such a motion, the Schrodinger equation can be solved. Graduate and senior undergraduate students in Physics, or engineering students, who intend to do research in Physics should find this book useful.
The aim of the present work is twofold: On one hand it considers the treatment of time observables in quantum mechanics. In particular, it is concerned with the application of a particular spin-boson detector model to arrival and passage times. Thus, it helps to illuminate the fundamental issue of how to treat time in quantum mechanics. In this course some interesting questions of quantum measurement theory are discussed by particular examples. On the other hand it explores the possibility of extending the quantum jump approach to a model beyond its original, quantum optical framework. It also examines by means of numerical examples whether the quantum jump approach, which employs a continuum of bath modes, promises to provide a good approximation to situations where one actually has to deal with a number of discrete bath modes.
Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane waves. This explanation was proposed by the author in 1963 when the author had been studying Quantum Mechanics. Self-action in a system of elementary particles, charged with elementary charges, is discussed in detail. This self-action is not taken in account in Quantum Mechanics, because otherwise experimental data (including data on atomic spectra) could not be theoretically explained. In Quantum Mechanics sometimes there is an electrostatic field without any electrostatic energy stored in it, and electrostatic negative energy with no charge and no electrostatic field, like in a positronium. Criteria for low-dimensional quantum movements are derived, quantum and classical rotations of modern objects are regarded. Simplified theory of polarons and bipolarins is proposed, and simple explanation of coexistence of zero angular momentum and non-zero magnetic moment in many-electron system is discussed.
In quantum mechanics, there are many counter-intuitive phenomena comparing with classical mechanics. In this book, we consider the two methods to compare the classical and the quantum systems. One is to quantitatively characterize the counter-factual phenomena in quantum mechanics related to the classical logic. We show that the weak value, which was initiated and developed by Yakir Aharonov and his colleagues and is an experimental accessible quantity, can characterize them by a simple example. We propose that the weak value is interpreted as a fundamental quantity to reformulate the quantum theory to obtain that the weak value can be derived from the observable-independent probability space in the sense of the Kolmogorov probability theory. The other content is the discrete time quantum walk (DTQW), which is defined as a quantum-mechanical analogue of the random walk. We obtain the analytical expression for the limit distribution of the one-dimensional DTQW with a two-dimensional coin. Under the simple decoherence model, we show that the DTQW is linearly related to the classical random walk. We also obtain that the DTQW can be taken as the quantum dynamical simulator.
Build an intuitive understanding of the principles behind quantum mechanics through practical construction and replication of original experiments With easy-to-acquire, low-cost materials and basic knowledge of algebra and trigonometry, Exploring Quantum Physics through Hands-on Projects takes readers step by step through the process of re-creating scientific experiments that played an essential role in the creation and development of quantum mechanics. Presented in near chronological order—from discoveries of the early twentieth century to new material on entanglement—this book includes question- and experiment-filled chapters on: Light as a Wave Light as Particles Atoms and Radioactivity The Principle of Quantum Physics Wave/Particle Duality The Uncertainty Principle Schrödinger (and his Zombie Cat) Entanglement From simple measurements of Planck's constant to testing violations of Bell's inequalities using entangled photons, Exploring Quantum Physics through Hands-on Projects not only immerses readers in the process of quantum mechanics, it provides insight into the history of the field—how the theories and discoveries apply to our world not only today, but also tomorrow. By immersing readers in groundbreaking experiments that can be performed at home, school, or in the lab, this first-ever, hands-on book successfully demystifies the world of quantum physics for all who seek to explore it—from science enthusiasts and undergrad physics students to practicing physicists and engineers.
The book presents some aspects of noncommutative quantum mechanics and field theory. It introduces the basic mathematical formalism of noncommutative quantum mechanics. In particular it reviews the procedure of Weyl quantization which is an useful technique for translating an ordinary field theory into a noncommutative one. Then as a preliminary exercise, it is demonstrated how noncommuting structures can be obtained in the first place by exploiting the reparametrization symmetry of particle models. Then it goes to investigate various other problems in these areas, namely, the construction of a one parameter family of noncommutative quantum theories dual to a commutative theory. The book should be useful to anyone interested in knowing the basic aspects of this fascinating field of noncommutative quantum physics.
Key advancements in the understanding of the fundamental and universal Quantum Mechanics now lead the way towards realizing the long outstanding resolution to the idea that "Quantum Mechanics is capable of yielding its own interpretation". One seemingly simple consideration today opens new doors to significant progress and sensibility, and that is the the consideration of the quantum mechanical view of the decomposition of System into subsystems. Progress in the understanding of subsystems and how they conspire to make a whole is presented in terms of Quantum Correlations Relativity, the Parallel Occurrence of Decoherence, Preferred Local Structures for Bipartite Decompositions of a two-mode Open System, and the discovery of a limitation of the Nakajima-Zwanzig Projection Method in Open Systems Theory. Ultimately, we can now impose a limitation on, and forcefully question the long term viability of the Everett Interpretation.
The computing power in terms of speed and capacity of today's digital computers has improved tremendously in the last decade. This improvement came mainly due to a revolution in manufacturing technology by developing the ability to manufacture smaller devices and by integrating more devices on a single die. Further development of the current technology will be restricted by physical limits since it won't be possible to shrink devices beyond a certain size. Eventually, classical electrical circuits will encounter the barrier of quantum mechanics. The laws of quantum mechanics can be used for building computing systems that work on the principles of quantum mechanics. Thus quantum computing has drawn the interest of many top scientists in the world. Ion Trap technology is one of the most promising prospective technologies for building quantum computers. This technology allows the placement of qubits - ions in 1-, 2- and 3-dimensional regular structures. This book presents efficient algorithms and methodologies for designing reversible quantum circuits.
The book is essentially a result of the authors' attempt to generalize Dirac's elegant method of solving the eigenvalue problem of the linear harmonic oscillator by constructing raising and lowering operators. As such, students of elementary Quantum Mechanics will find Chapters II and III quite useful and illuminating. At many stages in the book the reader will find the power of the commutator algebra unfolding in an elegant manner, as in the original Dirac approach. See the lucid application of the technique to find the eigenvalues and eigenfunctions of the Kratzer oscillator algebraically A student of Advanced Quantum Mechanics will find, in Chapter III, an illustrious application of the celebrated Infeld-Hull factorization method to find a class of ladder operators which connect the eigenstates of a hierarchy of Hamiltonians like, but not the same as, the ones in Supersymmetric Quantum Mechanics. The book will be of interest to a large spectrum of students of Physics at the Master's degree level and graduate students entering a research career in Theoretical Physics and Quantum Chemistry.
The purpose of this work is to retrace the steps that were made by scientists of ‘900, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two decades, put in question the classical physics. In this context, the study of the electronic structure of hydrogen atom has been the main starting point for the formulation of the theory and, till now, remains the only real case for which the quantum equation of motion can be solved exactly. The results obtained by each theory will be discussed critically, highlighting limits and potentials that allowed the further development of the quantum theory.
An Introduction to Advanced Quantum Physics presents important concepts from classical mechanics, electricity and magnetism, statistical physics, and quantum physics brought together to discuss the interaction of radiation and matter, selection rules, symmetries and conservation laws, scattering, relativistic quantum mechanics, apparent paradoxes, elementary quantum field theory, electromagnetic and weak interactions, and much more. This book consists of two parts: Part 1 comprises the material suitable for a second course in quantum physics and covers: Electromagnetic Radiation and Matter Scattering Symmetries and Conservation Laws Relativistic Quantum Physics Special Topics Part 2 presents elementary quantum field theory and discusses: Second Quantization of Spin 1/2 and Spin 1 Fields Covariant Perturbation Theory and Applications Quantum Electrodynamics Each chapter concludes with problems to challenge the students’ understanding of the material. This text is intended for graduate and ambitious undergraduate students in physics, material sciences, and related disciplines.
The possibility of using quantum sets in quantum mechanics was considered long ago. In this book we consider fractal Cantorian sets and emphasize the role of the empty set in physics and the crucial difference between the zero and the empty set. The quantum particle is represented by a Cantorian zero set while the quantum wave is represented by an empty Cantorian set. The new quantum entanglement theory is presented generalizing Einstein’s energy equation to an effective quantum gravity formula predicting accurately the actually measured cosmic energy content of the universe. The energy given by Einstein’s famous formula consists of two parts. The first part is the ordinary energy of the quantum particle modelled by the topology of the zero set. The second part is the dark energy of the quantum wave modelled by the topology of the empty set.
An invaluable introduction to nanomaterials and their applications Offering the unique approach of applying traditional physics concepts to explain new phenomena, Introduction to Nanomaterials and Devices provides readers with a solid foundation on the subject of quantum mechanics and introduces the basic concepts of nanomaterials and the devices fabricated from them. Discussion begins with the basis for understanding the basic properties of semiconductors and gradually evolves to cover quantum structures—including single, multiple, and quantum wells—and the properties of nanomaterial systems, such as quantum wires and dots. Written by a renowned specialist in the field, this book features: An introduction to the growth of bulk semiconductors, semiconductor thin films, and semiconductor nanomaterials Information on the application of quantum mechanics to nanomaterial structures and quantum transport Extensive coverage of Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein stastistics An in-depth look at optical, electrical, and transport properties Coverage of electronic devices and optoelectronic devices Calculations of the energy levels in periodic potentials, quantum wells, and quantum dots Introduction to Nanomaterials and Devices provides essential groundwork for understanding the behavior and growth of nanomaterials and is a valuable resource for students and practitioners in a field full of possibilities for innovation and invention.
This two-volume book series is an attempt to formulate a consistent relativistic quantum theory of interacting charged particles. The major construction will be undertaken in the second volume. Our goal in this first volume is to prepare the reader for that effort. Here we will introduce notation, terminology, and basic ideas of relativistic quantum theories. Our discussion will proceed systematically and, more or less traditionally, from the principle of relativity and postulates of measurements to the renormalization in quantum electrodynamics. This will cover material usually found in textbooks on quantum field theory. However, we will choose particles (rather than fields) as our basic ingredients. Quantum fields will be regarded as mere mathematical tools, which are convenient for building relativistically invariant and cluster separable particle interactions. The reader is expected to have a good grasp of non-relativistic quantum mechanics.