This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

This comprehensive textbook provides the fundamental concepts and methods of dissipative quantum mechanics and related issues in condensed matter physics starting from first principles. It deals with the phenomena and theory of decoherence, relaxation and dissipation in quantum mechanics that arise from the random exchange of energy with the environment. Major theoretical advances in combination with stunning experimental achievements and the arising perspective for quantum computing have brightened the field and brought it to the attention of the general community in natural sciences. Expertise in dissipative quantum mechanics is by now beneficial in a broad sphere.This book - originally published in 1992 and republished as enlarged and updated second, third and fourth edition in 1999, 2008, and 2012 - dives even deeper into the fundamental concepts, methods and applications of quantum dissipation. The fifth edition provides a self-contained and updated account of the quantum mechanics and quantum statistics of open systems. The subject matter of the book has been thoroughly revised to better comply with the needs of newcomers and the demands of the advanced readership. Most of the chapters are rewritten to enhance clarity and topicality. Four new chapters covering recent developments in the field have been added. There are about 600 references. This book is intended for use by advanced undergraduate and graduate students in physics, and for researchers active in the field. They will find the monograph as a rich and stimulating source.

This comprehensive textbook provides the fundamental concepts and methods of dissipative quantum mechanics and related issues in condensed matter physics starting from first principles. It deals with the phenomena and theory of decoherence, relaxation and dissipation in quantum mechanics that arise from the random exchange of energy with the environment. Major theoretical advances in combination with stunning experimental achievements and the arising perspective for quantum computing have brightened the field and brought it to the attention of the general community in natural sciences. Expertise in dissipative quantum mechanics is by now beneficial in a broad sphere.This book - originally published in 1992 and republished as enlarged and updated second, third and fourth edition in 1999, 2008, and 2012 - dives even deeper into the fundamental concepts, methods and applications of quantum dissipation. The fifth edition provides a self-contained and updated account of the quantum mechanics and quantum statistics of open systems. The subject matter of the book has been thoroughly revised to better comply with the needs of newcomers and the demands of the advanced readership. Most of the chapters are rewritten to enhance clarity and topicality. Four new chapters covering recent developments in the field have been added. There are about 600 references. This book is intended for use by advanced undergraduate and graduate students in physics, and for researchers active in the field. They will find the monograph as a rich and stimulating source.

This book focuses on the gradual formation of the concept of 'light quanta' or 'photons', as they have usually been called in English since 1926. The great number of synonyms that have been used by physicists to denote this concept indicates that there are many different mental models of what 'light quanta' are: simply finite, 'quantized packages of energy' or 'bullets of light'? 'Atoms of light' or 'molecules of light'? 'Light corpuscles' or 'quantized waves'? Singularities of the field or spatially extended structures able to interfere? 'Photons' in G.N. Lewis's sense, or as defined by QED, i.e. virtual exchange particles transmitting the electromagnetic force? The term 'light quantum' made its first appearance in Albert Einstein's 1905 paper on a "heuristic point of view" to cope with the photoelectric effect and other forms of interaction of light and matter, but the mental model associated with it has a rich history both before and after 1905. Some of its semantic layers go as far back as Newton and Kepler, some are only fully expressed several decades later, while others initially increased in importance then diminished and finally vanished. In conjunction with these various terms, several mental models of light quanta were developed-six of them are explored more closely in this book. It discusses two historiographic approaches to the problem of concept formation: (a) the author's own model of conceptual development as a series of semantic accretions and (b) Mark Turner's model of 'conceptual blending'. Both of these models are shown to be useful and should be explored further. This is the first historiographically sophisticated history of the fully fledged concept and all of its twelve semantic layers. It systematically combines the history of science with the history of terms and a philosophically inspired history of ideas in conjunction with insights from cognitive science.

This first of a kind textbook provides computational tools in Fortran 90 that are fundamental to quantum information, quantum computing, linear algebra and one dimensional spin half condensed matter systems. Over 160 subroutines are included, and the numerical recipes are aided by detailed flowcharts. Suitable for beginner and advanced readers alike, students and researchers will find this textbook to be a helpful guide and a compendium. Key Features: Includes 160 subroutines all of which can be used either as a standalone program or integrated with any other main program without any issues. Every parameter in the input, output and execution has been provided while keeping both beginner and advanced users in mind. The output of every program is explained thoroughly with detailed examples. A detailed dependency chart is provided for every recipe.

In the past four decades, there has been growing interest in the exciting new topic of physics in low dimensions. Thousands of original ideas have been proposed in the literature, and some are confirmed experimentally, along with several Nobel prizes which have been awarded in this field. While there are several books available, almost all are technical and accessible only to expert researchers. This book provides an accessible introduction to the field, with less emphasis on technical details. Whilst this book does not provide a traditional history of nano-science, instead it uses simple explanations and case studies as vehicles to explain key discoveries and the importance of them, enabling readers without a background in the area to gain an understanding of some aspects of nanoscale physics. It will be of interest to researchers working in condensed matter physics, in addition to engineers and advanced students in those disciplines. It also remains accessible to 'physics enthusiasts' from other academic disciplines, as technical details are contained within boxes and footnotes which can be skipped for a general reading of the book. Features: - Provides an accessible introduction to a technical subject - Contains exciting developments from the cutting-edge science being conducted in the area - Authored by a recognised expert in the field

The author has published two texts on classical physics, Introduction to Classical Mechanics and Introduction to Electricity and Magnetism, both meant for initial one-quarter physics courses. The latter is based on a course taught at Stanford several years ago with over 400 students enrolled. These lectures, aimed at the very best students, assume a good concurrent course in calculus; they are otherwise self-contained. Both texts contain an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the solutions to these problems have now been published in additional texts.A third published text completes the first-year introduction to physics with a set of lectures on Introduction to Quantum Mechanics, the very successful theory of the microscopic world. The Schroedinger equation is motivated and presented. Several applications are explored, including scattering and transition rates. The applications are extended to include quantum electrodynamics and quantum statistics. There is a discussion of quantum measurements. The lectures then arrive at a formal presentation of quantum theory together with a summary of its postulates. A concluding chapter provides a brief introduction to relativistic quantum mechanics. An extensive set of accessible problems again enhances and extends the coverage. The current book provides the solutions to those problems.The goal of these three texts is to provide students and teachers alike with a good, understandable, introduction to the fundamentals of classical and quantum physics.

The author has published two texts on classical physics, Introduction to Classical Mechanics and Introduction to Electricity and Magnetism, both meant for initial one-quarter physics courses. The latter is based on a course taught at Stanford several years ago with over 400 students enrolled. These lectures, aimed at the very best students, assume a good concurrent course in calculus; they are otherwise self-contained. Both texts contain an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the solutions to these problems have now been published in additional texts.A third published text completes the first-year introduction to physics with a set of lectures on Introduction to Quantum Mechanics, the very successful theory of the microscopic world. The Schroedinger equation is motivated and presented. Several applications are explored, including scattering and transition rates. The applications are extended to include quantum electrodynamics and quantum statistics. There is a discussion of quantum measurements. The lectures then arrive at a formal presentation of quantum theory together with a summary of its postulates. A concluding chapter provides a brief introduction to relativistic quantum mechanics. An extensive set of accessible problems again enhances and extends the coverage. The current book provides the solutions to those problems.The goal of these three texts is to provide students and teachers alike with a good, understandable, introduction to the fundamentals of classical and quantum physics.

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 Schroedinger'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 Schroedinger 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.

How to see physics in its full picture? This book offers a new approach: start from math, in its simple and elegant tools: discrete math, geometry, and algebra, avoiding heavy analysis that might obscure the true picture. This will get you ready to master a few fundamental topics in physics: from Newtonian mechanics, through relativity, towards quantum mechanics.Thanks to simple math, both classical and modern physics follow and make a complete vivid picture of physics. This is an original and unified point of view to highlighting physics from a fresh pedagogical angle.Each chapter ends with a lot of relevant exercises. The exercises are an integral part of the chapter: they teach new material and are followed by complete solutions. This is a new pedagogical style: the reader takes an active part in discovering the new material, step by step, exercise by exercise.The book could be used as a textbook in undergraduate courses such as Introduction to Newtonian mechanics and special relativity, Introduction to Hamiltonian mechanics and stability, Introduction to quantum physics and chemistry, and Introduction to Lie algebras with applications in physics.

How to see physics in its full picture? This book offers a new approach: start from math, in its simple and elegant tools: discrete math, geometry, and algebra, avoiding heavy analysis that might obscure the true picture. This will get you ready to master a few fundamental topics in physics: from Newtonian mechanics, through relativity, towards quantum mechanics.Thanks to simple math, both classical and modern physics follow and make a complete vivid picture of physics. This is an original and unified point of view to highlighting physics from a fresh pedagogical angle.Each chapter ends with a lot of relevant exercises. The exercises are an integral part of the chapter: they teach new material and are followed by complete solutions. This is a new pedagogical style: the reader takes an active part in discovering the new material, step by step, exercise by exercise.The book could be used as a textbook in undergraduate courses such as Introduction to Newtonian mechanics and special relativity, Introduction to Hamiltonian mechanics and stability, Introduction to quantum physics and chemistry, and Introduction to Lie algebras with applications in physics.

The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory. To advantage students, instructors and practitioners, and since the field is highly interdisciplinary, this book presents an introduction with all the basic notions in the same place. The field has seen a large development in parallel with the neighboring fields of quantum information, computation and communication. The author has maintained an introductory level to encourage course use. After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. Changes to the New Edition: New Chapter 4: Uncontrollable Systems and Dynamical Decomposition New section on quantum control landscapes A brief discussion of the experiments that earned the 2012 Nobel Prize in Physics Corrections and revised concepts are made to improve accuracy Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematics, physics and engineering work.

The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

There is no sharp dividing line between the foundations of physics and philosophy of physics. This is especially true for quantum mechanics. The debate on the interpretation of quantum mechanics has raged in both the scientific and philosophical communities since the 1920s and continues to this day. (We shall understand the unqualified term 'quantum mechanics' to mean the mathematical formalism, i. e. laws and rules by which empirical predictions and theoretical advances are made. ) There is a popular rendering of quantum mechanics which has been publicly endorsed by some well known physicists which says that quantum mechanics is not only 1 more weird than we imagine but is weirder than we can imagine. Although it is readily granted that quantum mechanics has produced some strange and counter-intuitive results, the case will be presented in this book that quantum mechanics is not as weird as we might have been led to believe! The prevailing theory of quantum mechanics is called Orthodox Quantum Theory (also known as the Copenhagen Interpretation). Orthodox Quantum Theory endows a special status on measurement processes by requiring an intervention of an observer or an observer's proxy (e. g. a measuring apparatus). The placement of the observer (or proxy) is somewhat arbitrary which introduces a degree of subjectivity. Orthodox Quantum Theory only predicts probabilities for measured values of physical quantities. It is essentially an instrumental theory, i. e.

This introduction to quantum mechanics is intended for undergraduate students of physics, chemistry, and engineering with some previous exposure to quantum ideas. Following in Heisenberg's and Dirac's footsteps, this book is centered on the concept of the quantum state as an embodiment of all experimentally available information about a system, and its representation as a vector in an abstract Hilbert space. This conceptual framework and formalism are introduced immediately, and developed throughout the first four chapters, while the standard Schroedinger equation does not appear until Chapter 5. The book grew out of lecture notes developed by the author over fifteen years of teaching at the undergraduate level. In response to numerous requests by students, material is presented with an unprecedented level of detail in both derivation of technical results and discussion of their physical significance. The book is written for students to enjoy reading it, rather than to use only as a source of formulas and examples. The colloquial and personal writing style makes it easier for readers to connect with the material. Additionally, readers will find short, relatable snippets about the "founding fathers" of quantum theory, their difficult historical circumstances, personal failings and triumphs, and often tragic fate. This textbook, complete with extensive original end-of-chapter exercises, is recommended for use in one- or two-semester courses for upper level undergraduate and beginning graduate students in physics, chemistry, or engineering.

From the international bestselling author of Physics of the Impossible and Physics of the Future.

This is the story of a quest: to find a Theory of Everything. Einstein dedicated his life to seeking this elusive Holy Grail, a single, revolutionary 'god equation' which would tie all the forces in the universe together, yet never found it. Some of the greatest minds in physics took up the search, from Stephen Hawking to Brian Greene. None have yet succeeded.

In The God Equation, renowned theoretical physicist Michio Kaku takes the reader on a mind-bending ride through the twists and turns of this epic journey: a mystery that has fascinated him for most of his life. He guides us through the key debates in modern physics, from Newton's law of gravity via relativity and quantum mechanics to the latest developments in string theory. It is a tale of dazzling breakthroughs and crushing dead ends, illuminated by Kaku's clarity, storytelling flair and infectious enthusiasm.

The object of the quest is now within sight: we are closer than ever to achieving the most ambitious undertaking in the history of science. If successful, the Theory of Everything could simultaneously unlock the deepest mysteries of space and time, and fulfil that most ancient and basic of human desires - to understand the meaning of our lives.

This collection of solved problems corresponds to the standard topics covered in established undergraduate and graduate courses in Quantum Mechanics. Completely up-to-date, problems are also included on topics of current interest which are absent in the existing literature. Solutions are presented in considerable detail, to enable students to follow each step. The emphasis is on stressing the principles and methods used, allowing students to master new ways of thinking and problem-solving techniques. The problems themselves are longer than those usually encountered in textbooks and consist of a number of questions based around a central theme, highlighting properties and concepts of interest. For undergraduate and graduate students, as well as those involved in teaching Quantum Mechanics, the book can be used as a supplementary text or as an independent self-study tool.

First published in 1993: This book is an outgrowth of fiber optic design courses given by the author.

The author has published two texts on classical physics, Introduction to Classical Mechanics and Introduction to Electricity and Magnetism, both meant for initial one-quarter physics courses. The latter is based on a course taught at Stanford several years ago with over 400 students enrolled. These lectures, aimed at the very best students, assume a good concurrent course in calculus; they are otherwise self-contained. Both texts contain an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the solutions to these problems have now been published in additional texts.The present text completes the first-year introduction to physics with a set of lectures on Introduction to Quantum Mechanics, the very successful theory of the microscopic world. The Schroedinger equation is motivated and presented. Several applications are explored, including scattering and transition rates. The applications are extended to include quantum electrodynamics and quantum statistics. There is a discussion of quantum measurements. The lectures then arrive at a formal presentation of quantum theory together with a summary of its postulates. A concluding chapter provides a brief introduction to relativistic quantum mechanics. An extensive set of accessible problems again enhances and extends the coverage.The goal of these three texts is to provide students and teachers alike with a good, understandable, introduction to the fundamentals of classical and quantum physics.

The author has published two texts on classical physics, Introduction to Classical Mechanics and Introduction to Electricity and Magnetism, both meant for initial one-quarter physics courses. The latter is based on a course taught at Stanford several years ago with over 400 students enrolled. These lectures, aimed at the very best students, assume a good concurrent course in calculus; they are otherwise self-contained. Both texts contain an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the solutions to these problems have now been published in additional texts.The present text completes the first-year introduction to physics with a set of lectures on Introduction to Quantum Mechanics, the very successful theory of the microscopic world. The Schroedinger equation is motivated and presented. Several applications are explored, including scattering and transition rates. The applications are extended to include quantum electrodynamics and quantum statistics. There is a discussion of quantum measurements. The lectures then arrive at a formal presentation of quantum theory together with a summary of its postulates. A concluding chapter provides a brief introduction to relativistic quantum mechanics. An extensive set of accessible problems again enhances and extends the coverage.The goal of these three texts is to provide students and teachers alike with a good, understandable, introduction to the fundamentals of classical and quantum physics.

In the last several decades, the quantum Hall effect has provided a remarkable platform for manipulating one-dimensional electronic modes and investigating fundamental physical phenomena. However, certain limitations make it difficult for various kinds of interesting modes structures to be formed using this platform. One example is the so called helical mode structure, in which two one-dimensional, counter propagating modes have opposite spins and thus spin and momentum are locked. Such helical modes have lately attracted significant interest, since, when coupled to a conventional superconductor, they are expected to manifest topological superconductivity and host Majorana zero modes. Even more interesting are fractional helical modes, which open the way for realizing generalized parafermionic zero modes. Possessing non-abelian exchange statistics, these quasiparticles may serve as building blocks in topological quantum computing. Here we present a new platform for manipulating integer and fractional quantum Hall edge modes, which allows the formation of robust one-dimensional helical as well as fractional helical modes. The platform is based on a carefully designed double-quantum-well structure in a GaAs based system hosting two electronic sub-bands in the quantum Hall effect regime. By electrostatic gating of different areas of the structure, counter-propagating integer, as well as fractional, edge modes with opposite spins are formed and their spin protection is verified. Beyond the formation of helical modes, the new platform can serve as a rich playground for new research. Some new possibilities include the artificial induction of compounded fractional edge modes and the construction of new edge mode-based interferometers.

This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations. Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.