Quantum Mechanics I - The Fundamentals

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Requiring no prior knowledge of the subject, this textbook provides a complete introduction to basic concepts and methods of quantum mechanics. Fully worked, step-by-step examples and end-of-chapter problem sets illustrate the application of formalism to physical problems and develop students' ability to solve problems. The text addresses core topics, including Schrodinger wave mechanics, the Heisenberg uncertainty principle, and the hydrogen atom, as well as recent theoretical developments and experimental research breakthroughs.

Inhaltsverzeichnis

Why Was Quantum Mechanics Developed? Schrödinger Equation and Wave Function. Operators, Eigenvalues, Eigenfunctions, and Wave Function. Exactly Solvable Systems I: Bound States. Exactly Solvable Systems II: Scattering States. Matrix Mechanics. Various Pictures in Quantum Mechanics and Density Matrix. Heisenberg Uncertainty Principle. Momentum Representation. Wave Packet. Theory of Angular Momentum. Hydrogen Atom. Approximation Methods I: Time-Independent Perturbation Theory. Approximation Methods II: Time-Dependent Perturbation Theory. Approximation Methods III: WKB and Asymptotic Methods. Approximation Methods IV: Variational Method. Scattering Theory. Identical Particles. Relativistic Quantum Theory. Mysteries in Quantum Mechanics. Numerical Methods for Quantum Mechanics. Appendices. Index.

Über den Autor / die Autorin

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.

Zusammenfassung

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.
The text addresses many topics not typically found in books at this level, including:

• Bound state solutions of quantum pendulum
• Pöschl–Teller potential
• 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
• Hydrogen atom in D-dimension
• Alternate perturbation theories
• An asymptotic method for slowly varying potentials
• Klein paradox, Einstein-Podolsky-Rosen (EPR) paradox, and Bell’s theorem
• 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.
Print Versions of this book also include access to the ebook version.

Zusatztext

"The first volume of this course of quantum mechanics contains basic concepts of quantum mechanics, mathematical formalism, and a wide range of applications to physically important systems. The problems concerning the considered subject are included at the end of each chapter. The textbook is intended for graduate students and also as a reference book. Doubtless advantage of this tutorial is the discussion of such mysteries in quantum mechanics as the collapse of the wave function, Einstein-Podolsky-Rosen paradox, hidden variables, the paradox of Schrödinger cat, and Bell's theorem. It should be noted the presence of numerical methods in quantum mechanics."—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
Vol I quote: "The real strength of this book lies in its scope. Each individual chapter covers the fundamentals of a topic and acts as an excellent reference for quantum researchers….I will certainly ensure that a copy remains on my bookshelf, for when I have a query on any fundamental aspect of quantum mechanics." —Contemporary Physics (Nov 2017), review by Prof. Thomas Collier, University of Exeter

Vol II quote: "I found digesting the latter part of this book a most enjoyable experience. Indeed, the final chapters on broad applications of advanced quantum mechanics are entertaining to read and refrain from delving too deeply into the intricacies. The reader is given an enticing glimpse of the research directions one might apply the knowledge of quantum mechanics presented over the two volumes. As with the first volume, I will keep this book close at hand for when I require a concise and mathematically rich guide to these advanced topics of quantum mechanics." —Contemporary Physics (Nov 2017), review by Prof. Thomas Collier, University of Exeter