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Quantum Mechanics Of The Anharmonic Oscillator
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Book Synopsis Quantum Anharmonic Oscillator by : Alexander Turbiner
Download or read book Quantum Anharmonic Oscillator written by Alexander Turbiner and published by World Scientific. This book was released on 2023-02-24 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quartic anharmonic oscillator with potential V(x)= x² + g²x⁴ was the first non-exactly-solvable problem tackled by the newly-written Schrödinger equation in 1926. Since that time thousands of articles have been published on the subject, mostly about the domain of small g² (weak coupling regime), although physics corresponds to g² ~ 1, and they were mostly about energies.This book is focused on studying eigenfunctions as a primary object for any g². Perturbation theory in g² for the logarithm of the wavefunction is matched to the true semiclassical expansion in powers of ℏ: it leads to locally-highly-accurate, uniform approximation valid for any g²∈[0,∞) for eigenfunctions and even more accurate results for eigenvalues. This method of matching can be easily extended to the general anharmonic oscillator as well as to the radial oscillators. Quartic, sextic and cubic (for radial case) oscillators are considered in detail as well as quartic double-well potential.
Book Synopsis Quantum Mechanics of the Anharmonic Oscillator by : R. McWeeny
Download or read book Quantum Mechanics of the Anharmonic Oscillator written by R. McWeeny and published by . This book was released on 1947 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book University Physics written by OpenStax and published by . This book was released on 2016-11-04 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale.
Download or read book Harmonic Oscillator written by Moshinsky and published by CRC Press. This book was released on 1996-05-01 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed introduction to the principles of particle detectors used in physics, biology, and medicine. Introductory chapters review the interactions of particles and radiation with matter, introduce the principles of detector operation and describe different types of measurement. The main body of the book describes all currently used detectors and counters, including their basic principles, potential uses and limitations. Two chapters are dedicated to electronics (readout methods, monitoring, data acquisition) and data analysis. A final chapter gives examples of detector systems. Concludes with a glossary of terms, tables of units and physical constants, and a reference list. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Quantum Oscillators by : Paul Blaise
Download or read book Quantum Oscillators written by Paul Blaise and published by John Wiley & Sons. This book was released on 2011-08-24 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other physical topics. These properties are: time-independent behavior, reversible dynamics, thermal statistical equilibrium and irreversible evolution toward equilibrium, together with anharmonicity and anharmonic couplings. As an application of these intricate topics, special attention is devoted to infrared lineshapes of single and complex (undergoing Fermi resonance or Davydov coupling) damped H-bonded systems, providing key insights into this rapidly evolving area of chemical science. Quantum Oscillators is a long overdue update in the literature surrounding quantum oscillators, and serves as an excellent supplementary text in courses on IR spectroscopy and hydrogen bonding. It is a must-have addition to the library of any graduate or undergraduate student in chemical physics.
Book Synopsis Introduction to Classical and Quantum Harmonic Oscillators by : S. C. Bloch
Download or read book Introduction to Classical and Quantum Harmonic Oscillators written by S. C. Bloch and published by John Wiley & Sons. This book was released on 2013-03-29 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating concepts, key to understanding the physical universe and a linchpin in fields as diverse as mechanics, electromagnetics, electronics, optics, acoustics, and quantum mechanics. Complete with disk, Introduction to Classical and Quantum Harmonic Oscillators is a hands-on guide to understanding how harmonic oscillators function and the analytical systems used to describe them. Professionals and students in electrical engineering, mechanical engineering, physics, and chemistry will gain insight in applying these analytical techniques to even more complex systems. With the help of spreadsheets ready to run on Microsoft Excel (or easily imported to Quattro Pro or Lotus 1-2-3), users will be able to thoroughly and easily examine concepts and questions, of considerable difficulty and breadth, without painstaking calculation. The software allows users to imagine, speculate, and ask "what if .?" and then instantly see the answer. You're not only able to instantly visualize results but also to interface with data acquisition boards to import real-world information. The graphic capability of the software allows you to view your work in color and watch new results blossom as you change parameters and initial conditions. Introduction to Classical and Quantum Harmonic Oscillators is a practical, graphically enhanced excursion into the world of harmonic oscillators that lets the reader experience and understand their utility and unique contribution to scientific understanding. It also describes one of the enduring themes in scientific inquiry, begun in antiquity and with an as yet unimagined future.
Book Synopsis Quantum Theory of Anharmonic Effects in Molecules by : Konstantin V. Kazakov
Download or read book Quantum Theory of Anharmonic Effects in Molecules written by Konstantin V. Kazakov and published by Elsevier. This book was released on 2012-07-09 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented in a clear and straightforward analysis, this book explores quantum mechanics and the application of quantum mechanics to interpret spectral phenomena. Specifically, the book discusses the relation between spectral features in mid or rear infrared regions, or in Raman scattering spectrum, and interactions between molecules or molecular species such as molecular ions, and their respective motions in gaseous or crystalline conditions. Beginning with an overview of conventional methods and problems which arise in molecular spectroscopy, the second half of the book suggests original techniques to investigate the area. The treatment is based on rigorous quantum-mechanical theories and procedures that are readily implemented in either manual methods or with symbolic computational software. Offers a novel approach in its application to physical phenomena Concise and clear discussions of quantum-mechanical theories and spectrum analysis Provides both theories and applications
Book Synopsis Introduction to Perturbation Theory in Quantum Mechanics by : Francisco M. Fernandez
Download or read book Introduction to Perturbation Theory in Quantum Mechanics written by Francisco M. Fernandez and published by CRC Press. This book was released on 2000-09-19 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation
Book Synopsis Introduction to Quantum Mechanics by : H. J. W. Mller-Kirsten
Download or read book Introduction to Quantum Mechanics written by H. J. W. Mller-Kirsten and published by World Scientific. This book was released on 2006 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrdinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schrdinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many other potentials, Green's functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.
Download or read book Wave Mechanics written by Gunter Ludwig and published by Elsevier. This book was released on 2016-06-03 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave Mechanics discusses the quantum physical concepts of wave. The title accounts the development of quantum theory. The text first covers the historical development of quantum theory, and then proceeds to tackling the two routes to quantum mechanics. Next, the selection discusses the matrix mechanics and wave mechanics as representations of mathematical structures in Hubert space. The text also deals with the physical interpretation of quantum mechanics, along with the temporal development of the physical quantities. In the second part, the selection presents several papers in quantum mechanics. The book will be of great use to students and researchers of quantum physics.
Book Synopsis Oscillator Representation in Quantum Physics by : M. Dineykhan
Download or read book Oscillator Representation in Quantum Physics written by M. Dineykhan and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation ofmost problems of quantum physics leads to the solution of the Schrodinger equation with an appropriate interaction Hamiltonian or potential. However, the exact solutions are known for rather a restricted set of potentials, so that the standard eternal problem that faces us is to find the best effective approximation to the exact solution of the Schrodinger equation under consideration. In the most general form, this problem can be formulated as follows. Let a total Hamiltonian H describing a relativistic (quantum field theory) or a nonrelativistic (quantum mechanics) system be given. Our problem is to solve the Schrodinger equation Hlft = Enlftn, n i. e. , to find the energy spectrum {En} and the proper wave functions {lft } n including the'ground state or vacuum lft = 10). The main idea of any ap o proximation technique is to find a decomposition in such a way that Ha describes our physical system in the "closest to H" manner, and the Schrodinger equation HolJt. (O) = E(O)lJt. (O) n n n can be solved exactly. The interaction Hamiltonian HI is supposed to give small corrections to the zero approximation which can be calculated. In this book, we shall consider the problem of a strong coupling regime in quantum field theory, calculations ofpath or functional integrals over the Gaussian measure and spectral problems in quantum mechanics. Let us con sider these problems briefly.
Book Synopsis The Physics of Quantum Mechanics by : James Binney
Download or read book The Physics of Quantum Mechanics written by James Binney and published by Oxford University Press, USA. This book was released on 2013-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.
Book Synopsis Quantum Oscillators by : Paul Blaise
Download or read book Quantum Oscillators written by Paul Blaise and published by Wiley. This book was released on 2011-08-02 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other physical topics. These properties are: time-independent behavior, reversible dynamics, thermal statistical equilibrium and irreversible evolution toward equilibrium, together with anharmonicity and anharmonic couplings. As an application of these intricate topics, special attention is devoted to infrared lineshapes of single and complex (undergoing Fermi resonance or Davydov coupling) damped H-bonded systems, providing key insights into this rapidly evolving area of chemical science. Quantum Oscillators is a long overdue update in the literature surrounding quantum oscillators, and serves as an excellent supplementary text in courses on IR spectroscopy and hydrogen bonding. It is a must-have addition to the library of any graduate or undergraduate student in chemical physics.
Download or read book Wave Mechanics written by Gunter Ludwig and published by Elsevier. This book was released on 2018-03-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected Readings in Physics: Wave Mechanics provides information pertinent to the fundamental aspects of wave mechanics. This book discusses the discovery of quantum mechanics. Organized into two parts encompassing five chapters and eight papers, this book begins with an overview of the essential parts of a theory, including a mathematical system, a domain of determinable facts, and a system of prescriptions correlating mathematical quantities and physical facts. This text then describes the classical model of electrons as mass points. Other chapters consider the connections between mathematically calculated quantities and physically measured quantities. This book discusses as well the relationship between the concepts of frequency and energy. The final paper deals with the theory of collision processes in which the transition probabilities are determined by the asymptomatic behavior of aperiodic solutions. This book is a valuable resource for physicists, scientists, and research workers.
Author :Harald J W Muller-kirsten Publisher :World Scientific Publishing Company ISBN 13 :9814397768 Total Pages :942 pages Book Rating :4.8/5 (143 download)
Book Synopsis Introduction To Quantum Mechanics: Schrodinger Equation And Path Integral (Second Edition) by : Harald J W Muller-kirsten
Download or read book Introduction To Quantum Mechanics: Schrodinger Equation And Path Integral (Second Edition) written by Harald J W Muller-kirsten and published by World Scientific Publishing Company. This book was released on 2012-07-19 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.
Book Synopsis A New Look at the Quantum Mechanics of the Harmonic Oscillator by : Hans A. Kastrup
Download or read book A New Look at the Quantum Mechanics of the Harmonic Oscillator written by Hans A. Kastrup and published by . This book was released on 2006 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Anharmonic Oscillator by : Alexander Turbiner
Download or read book Quantum Anharmonic Oscillator written by Alexander Turbiner and published by World Scientific. This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
