Some Unusual Topics In Quantum Mechanics

In this book, the author addresses selected topics in quantum mechanics that are not usually covered in books, but which are very helpful in developing a student's interest in, and a deeper understanding of the subject. The topics include two different ways of looking at quantum mechanics; three clarifying topics that students often find confusing; one classic theorem never proved in the classroom; and a discussion on whether there can be a non-linear quantum mechanics. The book can be used as supporting material for graduate-level core courses on quantum mechanics.

This second edition of Some Unusual Topics in Quantum Mechanics builds upon the topics covered in the first, with additional chapters that delve deeper into the mathematical foundations of the subject. New topics include Hilbert spaces and unbounded operators, minimum uncertainty states, path integrals in general coordinates, Fock spaces, second quantization, relativistic particle states, and quantum fields. Historical insights are also included, such as a pre-history of matrix mechanics and Pauli's proof of the H-atom spectrum using O(4) symmetry. Finally, readers are introduced to Bell's inequality and the non-locality in quantum mechanics that is revealed through its violation. These topics are rarely covered in introductory textbooks but are crucial to developing a student's interest and deeper understanding of quantum mechanics. This book serves as valuable supporting material for graduate-level core courses on the subject.

Quantum mechanics is one of the most fascinating, and at the same time most controversial, branches of contemporary science. Disputes have accompanied this science since its birth and have not ceased to this day. Uncommon Paths in Quantum Physics allows the reader to contemplate deeply some ideas and methods that are seldom met in the contemporary literature. Instead of widespread recipes of mathematical physics, based on the solutions of integro-differential equations, the book follows logical and partly intuitional derivations of non-commutative algebra. Readers can directly penetrate the abstract world of quantum mechanics. First book in the market that treats this newly developed area of theoretical physics; the book will thus provide a fascinating overview of the prospective applications of this area, strongly founded on the theories and methods that it describes. Provides a solid foundation for the application of quantum theory to current physical problems arising in the interpretation of molecular spectra and important effects in quantum field theory. New insight into the physics of anharmonic vibrations, more feasible calculations with improved precision.

This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

A fully updated edition of the classic text by acclaimed physicist A. Zee Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University

Quantum mechanics is a physical science dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles / waves. It also forms the basis for the contemporary understanding of how very large objects such as stars and galaxies, and cosmological events such as the Big Bang, can be analyzed and explained. Quantum mechanics is the foundation of several related disciplines including nanotechnology, condensed matter physics, quantum chemistry, structural biology, particle physics, and electronics. The term "quantum mechanics" was first coined by Max Born in 1924. The acceptance by the general physics community of quantum mechanics is due to its accurate prediction of the physical behaviour of systems, including systems where Newtonian mechanics fails. Even general relativity is limited -- in ways quantum mechanics is not -- for describing systems at the atomic scale or smaller, at very low or very high energies, or at the lowest temperatures. Through a century of experimentation and applied science, quantum mechanical theory has proven to be very successful and practical. The foundations of quantum mechanics date from the early 1800s, but the real beginnings of QM date from the work of Max Planck in 1900. Albert Einstein and Niels Bohr soon made important contributions to what is now called the "old quantum theory." However, it was not until 1924 that a more complete picture emerged with Louis de Broglie's matter-wave hypothesis and the true importance of quantum mechanics became clear. Some of the most prominent scientists to subsequently contribute in the mid-1920s to what is now called the "new quantum mechanics" or "new physics" were Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Erwin Schrödinger. Later, the field was further expanded with work by Julian Schwinger, Sin-Itiro Tomonaga and Richard Feynman for the development of Quantum Electrodynamics in 1947 and by Murray Gell-Mann in particular for the development of Quantum Chromodynamics. The interference that produces colored bands on bubbles cannot be explained by a model that depicts light as a particle. It can be explained by a model that depicts it as a wave. The drawing shows sine waves that resemble waves on the surface of water being reflected from two surfaces of a film of varying width, but that depiction of the wave nature of light is only a crude analogy. Early researchers differed in their explanations of the fundamental nature of what we now call electromagnetic radiation. Some maintained that light and other frequencies of electromagnetic radiation are composed of particles, while others asserted that electromagnetic radiation is a wave phenomenon. In classical physics these ideas are mutually contradictory. Ever since the early days of QM scientists have acknowledged that neither idea by itself can explain electromagnetic radiation. Despite the success of quantum mechanics, it does have some controversial elements. For example, the behaviour of microscopic objects described in quantum mechanics is very different from our everyday experience, which may provoke some degree of incredulity. Most of classical physics is now recognized to be composed of special cases of quantum physics theory and/or relativity theory. Dirac brought relativity theory to bear on quantum physics so that it could properly deal with events that occur at a substantial fraction of the speed of light. Classical physics, however, also deals with mass attraction (gravity), and no one has yet been able to bring gravity into a unified theory with the relativized quantum theory.

An advanced quantum mechanics textbook that provides a unique pedagogical introduction to high-level topics in the field.

Quirky Quantum Concepts explains the more important and more difficult concepts in theoretical quantum mechanics, especially those which are consistently neglected or confusing in many common expositions. The emphasis is on physical understanding, which is necessary for the development of new, cutting edge science. In particular, this book explains the basis for many standard quantum methods, which are too often presented without sufficient motivation or interpretation. The book is not a simplification or popularization: it is real science for real scientists. Physics includes math, and this book does not shy away from it, but neither does it hide behind it. Without conceptual understanding, math is gibberish. The discussions here provide the experimental and theoretical reasoning behind some of the great discoveries, so the reader may see how discoveries arise from a rational process of thinking, a process which Quirky Quantum Concepts makes accessible to its readers. Quirky Quantum Concepts is therefore a supplement to almost any existing quantum mechanics text. Students and scientists will appreciate the combination of conversational style, which promotes understanding, with thorough scientific accuracy.