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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.

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 SCHROEDINGER 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

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.

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 Schrodinger'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