Advances In One Dimensional Wave Mechanics
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Advances In One Dimensional Wave Mechanics
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Author : Zhuangqi Cao
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-16
Advances In One Dimensional Wave Mechanics written by Zhuangqi Cao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-16 with Science categories.
Advances in One-Dimensional Wave Mechanics provides a comprehensive description of the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Utilizing a deeper understanding of the wave nature of matter, this book introduces the concept of the scattered sub-waves and a series of new analytical results using the Analytical Transfer Matrix (ATM) method. This work will be useful for graduate students majoring in physics, mainly in basic quantum theory, as well as for academic researchers exploring electromagnetism, particle physics, and wave mechanics and for experts in the field of optical waveguide and integrated optics. Prof. Zhuangqi Cao is a Professor of Physics at Shanghai Jiao Tong University, China. Dr. Cheng Yin is a teacher at Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, China.
Advanced Quantum Mechanics
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Author : Rainer Dick
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-11
Advanced Quantum Mechanics written by Rainer Dick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-11 with Science categories.
Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. The textbook can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition amplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes. Quantization is first discussed for the Schrödinger field before the relativistic Maxwell, Klein-Gordon and Dirac fields are quantized. Quantized Schrödinger field theory is not only important for condensed matter physics and materials science, but also provides the easiest avenue to general field quantization and is therefore also useful for students with an interest in nuclear and particle physics. The quantization of the Maxwell field is performed in Coulomb gauge. This is the appropriate and practically most useful quantization procedure in condensed matter physics, chemistry, and materials science because it naturally separates the effects of Coulomb interactions, exchange interactions, and photon scattering. The appendices contain additional material that is usually not found in standard quantum mechanics textbooks, including a completeness proof of eigenfunctions of one-dimensional Sturm-Liouville problems, logarithms of matrices, and Green's functions in different dimensions.
Advanced Quantum Mechanics The Classical Quantum Connection
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Author : Reinhold Blumel
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2010-04-28
Advanced Quantum Mechanics The Classical Quantum Connection written by Reinhold Blumel and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-28 with Science categories.
This book provides a coherent introduction to Gutzwiller’s trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, phyics, and engineering, this book is attractice for professional scientists and engineers as well. Following a thorough review of elementary concepts in classical and quantum mechanics the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller’s approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman’s path integrals. Numerous applications, including the exact solutions of “unsolvable” one-dimensional quantum problems, illustrate the power of Gutzwiller’s method. Worked examples throughout the text illustrate the material and provide immediate “hands-on” demonstrations of tools and concepts just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.
Advanced Quantum Mechanics
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Author : Reinhold Blümel
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2011-08-24
Advanced Quantum Mechanics written by Reinhold Blümel and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with Science categories.
Physics
Quantum Physics In One Dimension
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Author : Thierry Giamarchi
language : en
Publisher: Clarendon Press
Release Date : 2003-12-18
Quantum Physics In One Dimension written by Thierry Giamarchi and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-18 with Science categories.
This book presents in a pedagogical yet complete way correlated systems in one dimension. Recent progress in nanotechnology and material research have made one dimensional systems a crucial part of today's physics. After an introduction to the basic concepts of correlated systems, the book gives a step by step description of the techniques needed to treat one dimension, and discusses the resulting physics. Then specific experimental realizations of one dimensional systems such as spin chains, quantum wires, nanotubes, organic superconductors etc. are examined. Given its progressive and pedagogical approach, this book should satisfy both graduate students who want to learn the tools of the trade and become professionals in the field as well as more advanced researchers who want to know more about the physics of a specific one dimensional system without unnecessary technicalities.
Recent Developments In The Theory Of Wave Propagation
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Author : New York University. Institute for Mathematics and Mechanics
language : en
Publisher:
Release Date : 1950
Recent Developments In The Theory Of Wave Propagation written by New York University. Institute for Mathematics and Mechanics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Wave mechanics categories.
Wave Equations In Higher Dimensions
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Author : Shi-Hai Dong
language : en
Publisher: Springer
Release Date : 2011-07-09
Wave Equations In Higher Dimensions written by Shi-Hai Dong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-09 with Science categories.
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography.
Advanced Undergraduate Quantum Mechanics
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Author : Lev I. Deych
language : en
Publisher: Springer
Release Date : 2018-04-05
Advanced Undergraduate Quantum Mechanics written by Lev I. Deych and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-05 with Science categories.
This introduction to quantum mechanics is intended for undergraduate students of physics, chemistry, and engineering with some previous exposure to quantum ideas. Following in Heisenberg’s and Dirac’s footsteps, this book is centered on the concept of the quantum state as an embodiment of all experimentally available information about a system, and its representation as a vector in an abstract Hilbert space. This conceptual framework and formalism are introduced immediately, and developed throughout the first four chapters, while the standard Schrödinger equation does not appear until Chapter 5. The book grew out of lecture notes developed by the author over fifteen years of teaching at the undergraduate level. In response to numerous requests by students, material is presented with an unprecedented level of detail in both derivation of technical results and discussion of their physical significance. The book is written for students to enjoy reading it, rather than to use only as a source of formulas and examples. The colloquial and personal writing style makes it easier for readers to connect with the material. Additionally, readers will find short, relatable snippets about the “founding fathers” of quantum theory, their difficult historical circumstances, personal failings and triumphs, and often tragic fate. This textbook, complete with extensive original end-of-chapter exercises, is recommended for use in one- or two-semester courses for upper level undergraduate and beginning graduate students in physics, chemistry, or engineering.
Selected Topics In Nonlinear Wave Mechanics
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Author : C.I. Christov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Selected Topics In Nonlinear Wave Mechanics written by C.I. Christov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.
Advanced Concepts In Quantum Mechanics
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Author : Giampiero Esposito
language : en
Publisher: Cambridge University Press
Release Date : 2015
Advanced Concepts In Quantum Mechanics written by Giampiero Esposito and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Science categories.
This book introduces a geometric view of fundamental physics, ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics.