Factorization Method In Quantum Mechanics
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| Author | : Shi-Hai Dong |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 308 |
| Release | : 2007-04-01 |
| Genre | : Science |
| ISBN | : 1402057962 |
This book introduces the factorization method in quantum mechanics at an advanced level, with the aim of putting mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader’s disposal. For this purpose, the text provides a comprehensive description of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in quantum mechanics textbooks.
| Author | : Thomas Edward Hull |
| Publisher | : |
| Total Pages | : |
| Release | : 1949 |
| Genre | : |
| ISBN | : |
| Author | : H. R. Coish |
| Publisher | : |
| Total Pages | : |
| Release | : 1946 |
| Genre | : |
| ISBN | : |
| Author | : Kevin Costello |
| Publisher | : Cambridge University Press |
| Total Pages | : 399 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 1107163102 |
This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.
| Author | : K.T. Hecht |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 768 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461212723 |
Intended for beginning graduate students, this text takes the reader from the familiar coordinate representation of quantum mechanics to the modern algebraic approach, emphasizing symmetry principles throughout. After an introduction to the basic postulates and techniques, the book discusses time-independent perturbation theory, angular momentum, identical particles, scatteering theory, and time-dependent perturbation theory. The whole is rounded off with several lectures on relativistic quantum mechanics and on many-body theory.
| Author | : Georg Junker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 179 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 364261194X |
The idea of supersymmetry was originally introduced in relativistic quantum field theories as a generalization of Poincare symmetry. In 1976 Nicolai sug gested an analogous generalization for non-relativistic quantum mechanics. With the one-dimensional model introduced by Witten in 1981, supersym metry became a major tool in quantum mechanics and mathematical, sta tistical, and condensed-IIll;l. tter physics. Supersymmetry is also a successful concept in nuclear and atomic physics. An underlying supersymmetry of a given quantum-mechanical system can be utilized to analyze the properties of the system in an elegant and effective way. It is even possible to obtain exact results thanks to supersymmetry. The purpose of this book is to give an introduction to supersymmet ric quantum mechanics and review some of the recent developments of vari ous supersymmetric methods in quantum and statistical physics. Thereby we will touch upon some topics related to mathematical and condensed-matter physics. A discussion of supersymmetry in atomic and nuclear physics is omit ted. However, the reader will find some references in Chap. 9. Similarly, super symmetric field theories and supergravity are not considered in this book. In fact, there exist already many excellent textbooks and monographs on these topics. A list may be found in Chap. 9. Yet, it is hoped that this book may be useful in preparing a footing for a study of supersymmetric theories in atomic, nuclear, and particle physics. The plan of the book is as follows.
| Author | : Mohsen Razavy |
| Publisher | : World Scientific |
| Total Pages | : 678 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 9814304107 |
This book provides a detailed account of quantum theory with a much greater emphasis on the Heisenberg equations of motion and the matrix method. No other texts have come close to discuss quantum theory in terms of depth of coverage. The book features a deeper treatment of the fundamental concepts such as the rules of constructing quantum mechanical operators and the classical-quantal correspondence; the exact and approximate methods based on the Heisenberg equations; the determinantal approach to the scattering theory and the LSZ reduction formalism where the latter method is used to obtain the transition matrix. The uncertainty relations for a number of different observables are derived and discussed. A comprehensive chapter on the quantization of systems with nonlocalized interaction is included. Exact solvable models, and approximate techniques for solution of realistic many-body problems are also considered. The book takes a unified look in the final chapter, examining the question of measurement in quantum theory, with an introduction to the Bell's inequalities.
| Author | : Leticia González |
| Publisher | : John Wiley & Sons |
| Total Pages | : 52 |
| Release | : 2021-02-01 |
| Genre | : Science |
| ISBN | : 1119417759 |
An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.
| Author | : Bijan Kumar Bagchi |
| Publisher | : CRC Press |
| Total Pages | : 242 |
| Release | : 2000-09-21 |
| Genre | : Science |
| ISBN | : 9781420035810 |
Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods. Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.
| Author | : O. L. De Lange |
| Publisher | : Oxford [England] : Clarendon Press ; Oxford ; New York : Oxford University Press |
| Total Pages | : 400 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : |
Quantum mechanical problems capable of exact solution are traditionally solved in a few instances only (such as the harmonic oscillator and angular momentum) by operator methods, but mainly by means of Schrodinger's wave mechanics. The present volume shows that a large range of one- and three- dimensional problems, including certain relativistic ones, are solvable by algebraic, representation-independent methods using commutation relations, shift operators, the viral, hyperviral, and Hellman-Feynman theorems. Applications of these operator methods to the calculation of eigenvalues, matrix elements, and wavefunctions are discussed in detail. This volume provides an outstanding introduction to the use of operator methods in quantum mechanics, and also serves as a reference work on this topic. As such it is an excellent complement to senior and graduate courses in quantum mechanics. Although primarily a book on applications of operator methods, the presentation is made self-contained by the inclusion of an introductory chapter on the formalism of quantum mechanics. Additional background material supplements the volume at various points in the text. Although there has been much research on operator methods to solve quantum mechanical problems, until now many of these results have remained scattered throughout the literature. Nonspecialists, as well as graduate and upper division students in physics will find this accessible volume to be essential reading in theoretical physics.
