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Quantum Mechanics II
Advanced Topics
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Quantum Mechanics II: Advanced Topics
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Book Description
Why the Quantum Field Theory?
Quantum Mechanics II: Advanced Topics
uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.Establishes a Need for the Quantum Field Theory
Consisting of ten chapters, this illuminating text:
- Covers the basic ideas of both classical and quantum field theories
- Highlights path integral formalism, supersymmetric quantum mechanics, coherent and squeezed states, Berry's phase, Aharonov-Bohm and Sagnac effects, and Wigner function
- Addresses basic principles, salient features, and applications
- Describes basic concepts of quantum computers, some of the quantum algorithms, and features of quantum computation
- Explores advances made in the field of quantum cryptography
- Provides a brief and compact introduction to topics of growing interest including quantum versions of theory of gravity, Zeno effect, teleportation, games, cloning, diffusion, and chaos
- Focuses on the theoretical aspects of various advanced topics
- Outlines some of the quantum technologies and/or technological applications of quantum phenomena
- Presents the basic principles and salient features of ghost imaging, detection of weak amplitude object and small displacements, entangled two-photon microscopy, quantum lithography, metrology, and teleportation of optical images
- Contains several worked-out problems at the end of each chapter
- Includes material that can be covered in an advanced course on quantum mechanics
Quantum Mechanics II: Advanced Topics
addresses the basic principles and current research on various topics in quantum mechanics, and is a valuable resource for advanced undergraduate and graduate students in physics, chemistry, and engineering with an interest in quantum mechanics.Print Versions of this book also include access to the ebook version.
Table of Contents
Quantum Field Theory
INTRODUCTION
WHY QUANTUM FIELD THEORY?
WHAT IS A FIELD?
CLASSICAL FIELD THEORY
QUANTUM EQUATIONS FOR FIELDS
QUANTIZATION OF NONRELATIVISTIC WAVE EQUATION
ELECTROMAGNETIC FIELD IN VACUUM
INTERACTION OF CHARGED PARTICLES WITH ELECTROMAGNETIC FIELD
SPONTANEOUS EMISSION
QUANTIZATION OF KLEIN–GORDON EQUATION
QUANTIZATION OF DIRAC FIELD
GAUGE FIELD THEORIES
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Path Integral Formulation
INTRODUCTION
TIME EVOLUTION OF WAVE FUNCTION AND PROPAGATOR
PATH INTEGRAL REPRESENTATION OF PROPAGATOR
CONNECTION BETWEEN THE PROPAGATOR AND THE CLASSICAL ACTION
SCHRÖDINGER EQUATION FROM PATH INTEGRAL FORMULATION
TRANSITION AMPLITUDE OF A FREE PARTICLE
SYSTEMS WITH QUADRATIC LAGRANGIAN
PATH INTEGRAL FOR HARMONIC OSCILLATOR
PATH INTEGRAL VERSION OF EHRENFEST’S THEOREM
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Supersymmetric Quantum Mechanics
INTRODUCTION
SUPERSYMMETRIC POTENTIALS
RELATIONS BETWEEN THE EIGENSTATES OF TWO SUPERSYMMETRIC HAMILTONIANS
HIERARCHY OF SUPERSYMMETRIC HAMILTONIANS
APPLICATIONS
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Coherent and Squeezed States
INTRODUCTION
THE UNCERTAINTY PRODUCT OF HARMONIC OSCILLATOR
COHERENT STATES: DEFINITION AND UNCERTAINTY PRODUCT
PHYSICAL MEANING OF COHERENT STATES
GENERATION OF COHERENT STATES
PROPERTIES OF COHERENT STATES
SQUEEZED STATES
DEFORMED OSCILLATORS AND NONLINEAR COHERENT STATES
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Berry’s Phase, Aharonov–Bohm and Sagnac Effects
INTRODUCTION
DERIVATION OF BERRY’S PHASE
ORIGIN AND PROPERTIES OF BERRY’S PHASE
CLASSICAL ANALOGUE OF BERRY’S PHASE
EXAMPLES FOR BERRY’S PHASE
EFFECTS OF BERRY’S PHASE
APPLICATIONS OF BERRY’S PHASE
EXPERIMENTAL VERIFICATION OF BERRY’S PHASE
PANCHARATNAM’S WORK
THE AHARONOV–BOHM EFFECT
SAGNAC EFFECT
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Phase Space Picture and Canonical Transformations
INTRODUCTION
SQUEEZE AND ROTATION IN PHASE SPACE
LINEAR CANONICAL TRANSFORMATIONS
WIGNER FUNCTION
TIME EVOLUTION OF THE WIGNER FUNCTION
APPLICATIONS
ADVANTAGES OF THE WIGNER FUNCTION
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Quantum Computers
INTRODUCTION
WHAT IS A QUANTUM COMPUTER?
WHY IS A QUANTUM COMPUTER?
FUNDAMENTAL PROPERTIES
QUANTUM ALGORITHMS
FEATURES OF QUANTUM COMPUTATION
QUANTUM COMPUTATION THROUGH NMR
WHY IS MAKING A QUANTUM COMPUTER EXTREMELY DIFFICULT?
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
QUANTUM CRYPTOGRAPHY
INTRODUCTION
STANDARD CRYPTOSYSTEMS
QUANTUM CRYPTOGRAPHY–BASIC PRINCIPLE
TYPES OF QUANTUM CRYPTOGRAPHY
MULTIPARTY QUANTUM SECRET SHARING
APPLICATIONS OF QUANTUM CRYPTOGRAPHY
IMPLEMENTATION AND LIMITATIONS
FIBER-OPTICAL QUANTUM KEY DISTRIBUTION
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Some Other Advanced Topics
INTRODUCTION
QUANTUM THEORY OF GRAVITY
QUANTUM ZENO EFFECT
QUANTUM TELEPORTATION
QUANTUM GAMES
QUANTUM CLONING
QUANTUM DIFFUSION
QUANTUM CHAOS
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Quantum Technologies
INTRODUCTION
QUANTUM ENTANGLEMENT
QUANTUM ENTANGLED PHOTONS
GHOST IMAGING
DETECTION OF WEAK AMPLITUDE OBJECT
ENTANGLED TWO-PHOTON MICROSCOPY
DETECTION OF SMALL DISPLACEMENTS
QUANTUM LITHOGRAPHY
QUANTUM METROLOGY
QUANTUM TELEPORTATION OF OPTICAL
IMAGES
CONCLUDING REMARKS
BIBLIOGRAPHY
EXERCISES
Solutions to selected exercises
Index
Author(s)
Biography
S. Rajasekar received his B.Sc. and M.Sc. in physics both from the St. Joseph’s College, Tiruchirapalli. In 1987, he received his M.Phil. in physics from Bharathidasan University, Tiruchirapalli. He was awarded a Ph.D. in physics (nonlinear dynamics) from Bharathidasan University in 1992. In 2005, he became a professor at the School of Physics, Bharathidasan University. His recent research focuses on nonlinear dynamics with a special emphasis on nonlinear resonances. He has coauthored a book, and authored or coauthored more than 80 research papers in nonlinear dynamics.
R. Velusamy received his B.Sc. in physics from the Ayya Nadar Janaki Ammal College, Sivakasi in 1972 and M.Sc. in physics from the P.S.G. Arts and Science College, Coimbatore in 1974. He received an M.S. in electrical engineering at the Indian Institute of Technology, Chennai in the year 1981. In the same year, he joined in the Ayya Nadar Janaki Ammal College as an assistant professor in physics. He was awarded an M.Phil. in physics in 1988. He retired in 2010. His research topics are quantum confined systems and wave packet dynamics.
Reviews
"The second volume of this textbook contains many advanced topics of current research in quantum mechanics. The problems concerning the considered subject are included at the end of any chapter. The textbook is intended for graduate students and also as a reference book. Doubtless advantage of this tutorial is to have material on current research, such as supersymmetric quantum mechanics, coherent and squeezed states, Sagnac effect, quantum computers, quantum cryptography, and so on. A separate chapter is devoted to discussing some of the issues that are at the forefront of current research: quantum gravity, quantum Zeno effect, quantum teleportation, quantum games, quantum cloning, quantum diffusion, and quantum chaos."
—Zentralblatt MATH 1318"… excellent, up-to-date … can be used as either a two-to-three-semester graduate text or as a standalone reference book. Quantum Mechanics I: The Fundamentals covers the canonical basics and Quantum Mechanics II: Advanced Topics covers a range of modern developments from introductory quantum field theory through quantum information theory and other quantum technologies, such as quantum metrology and imaging, that are not discussed in other sources … I recommend this set highly."
—Dr. Jonathan P. Dowling, Hearne Professor of Theoretical Physics and Co-Director, Hearne Institute for Theoretical Physics, Louisiana State University, and Author of Schrödinger's Killer App: Race to Build the World's First Quantum Computer"Be assured … these two books by Rajasekar and Velusamy will definitely tell you how to do quantum mechanics."
—Dr. K.P.N. Murthy, Professor, School of Physics and Director, Centre for Integrated Studies, University of Hyderabad