Quantum Mechanics
Two Vol Set
Preview
Book Description
Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems. This fully updated new edition addresses many topics not typically found in books at this level, including: Bound state solutions of quantum pendulum Morse oscillator Solutions of classical counterpart of quantum mechanical systems A criterion for bound state Scattering from a locally periodic potential and reflection-less potential Modified Heisenberg relation Wave packet revival and its dynamics An asymptotic method for slowly varying potentials Klein paradox, Einstein-Podolsky-Rosen (EPR) paradox, and Bell’s theorem Delayed-choice experiments Fractional quantum mechanics Numerical methods for quantum systems A collection of problems at the end of each chapter develops students’ understanding of both basic concepts and the application of theory to various physically important systems. This book, along with the authors’ follow-up Quantum Mechanics II: Advanced Topics, provides students with a broad, up-to-date introduction to quantum mechanics. Quantum Mechanics II: Advanced Topics offers a comprehensive exploration of the state-of-the-art in various advanced topics of current research interest. A follow-up to the authors’ introductory book Quantum Mechanics I: The Fundamentals, this book expounds basic principles, theoretical treatment, case studies, worked-out examples and applications of advanced topics including quantum technologies. A thoroughly revised and updated this unique volume presents an in-depth and up-to-date progress on the growing topics including latest achievements on quantum technology. In the second edition six new chapters are included and the other ten chapters are extensively revised. Features Covers classical and quantum field theories, path integral formalism and supersymmetric quantum mechanics. Highlights coherent and squeezed states, Berry’s phase, Aharonov—Bohm effect and Wigner function. Explores salient features of quantum entanglement and quantum cryptography. Presents basic concepts of quantum computers and the features of no-cloning theorem and quantum cloning machines. Describes the theory and techniques of quantum tomography, quantum simulation and quantum error correction. Introduces other novel topics including quantum versions of theory of gravity, cosmology, Zeno effect, teleportation, games, chaos and steering. Outlines the quantum technologies of ghost imaging, detection of weak amplitudes and displacements, lithography, metrology, teleportation of optical images, sensors, batteries and internet. Contains several worked-out problems and exercises in each chapter. Quantum Mechanics II: Advanced Topics addresses various currently emerging exciting topics of quantum mechanics. It emphasizes the fundamentals behind the latest cutting-edge developments to help explain the motivation for deeper exploration. The book is a valuable resource for graduate students in physics and engineering wishing to pursue research in quantum mechanics.
Table of Contents
Volume I: 1. Why Was Quantum Mechanics Developed? 2. Schrödinger Equation and Wave Function. 3. Operators, Eigenvalues and Eigenfunctions. 4. Exactly Solvable Systems I: Bound States. 5. Exactly Solvable Systems II: Scattering States. 6. Matrix Mechanics. 7. Various Pictures in Quantum Mechanics and Density Matrix. 8. Heisenberg Uncertainty Principle. 9. Momentum Representation. 10. Wave Packet. 11. Theory of Angular Momentum. 12. Hydrogen Atom. 13. Approximation Methods I: Time-Independent Perturbation Theory. 14. Approximation Methods II: Time-Dependent Perturbation Theory. 15. Approximation Methods III: WKB and Asymptotic Methods. 16. Approximation Methods IV: Variational Method. 17. Scattering Theory. 18. Identical Particles. 19. Relativistic Quantum Theory. 20. Mysteries in Quantum Mechanics. 21. Delayed-Choice Experiments. 22. Fractional Quantum Mechanics. 23. Numerical Methods for Quantum Mechanics. Appendices. Index. Volume II: 1. Quantum Field Theory. 2. Path Integral Formulation. 3. Supersymmetric Quantum Mechanics. 4. Coherent and Squeezed States. 5. Berry’s Phase, Aharonov–Bohm and Sagnac Effects. 6. Phase Space Picture and Canonical Transformations. 7. Quantum Entanglement. 8. Quantum Decoherence. 9. Quantum Computers. 10. Quantum Cryptography. 11. No-Cloning Theorem and Quantum Cloning Machines. 12. Quantum Tomography. 13. Quantum Simulation. 14. Quantum Error Correction. 15. Some Other Advanced Topics. 16. Quantum Technologies. Solutions to Selected Exercises. Index.
Author(s)
Biography
S. Rajasekar received his B.Sc. and M.Sc. in Physics both from St. Joseph’s College, Tiruchirapalli. He was awarded his Ph.D. degree from Bharathidasan University in 1992 under the supervision of Prof. M. Lakshmanan. In 1993, he joined as a Lecturer at the Department of Physics, Manonmaniam Sundaranar University, Tirunelveli. In 2003, the book Nonlinear Dynamics: Integrability, Chaos and Patterns written by Prof. M. Lakshmanan and the author was published by Springer. In 2005, he joined as a Professor at the School of Physics, Bharathidasan University. In 2016 Springer published Nonlinear Resonances written by Prof. Miguel A.F. Sanjuan and the author. In 2021 Professors U.E. Vincent, P.V.E. McClintock, I.A. Khovanov and the author compiled and edited two issues of Philosophical Transactions of the Royal Society A on the theme Vibrational and Stochastic Resonances in Driven Nonlinear Systems. He has also edited Recent Trends in Chaotic, Nonlinear and Complex Dynamics with Professors Jan Awrejecewicz and Minvydas Ragulskis, published by World Scienti?c in 2022. His recent research focuses on nonlinear dynamics with a special emphasize on nonlinear resonances. He has authored or co-authored more than 120 research papers in nonlinear dynamics. R. Velusamy received his B.Sc. degree 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 worked as a demonstrator in the Department of Physics in P.S.G. Arts and Science College during 1974-77. He received an M.S. Degree in Electrical Engineering at 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 a M.Phil. degree in Physics in the year 1988. He retired in the year 2010. His research topics are quantum con?ned systems and wave packet dynamics.