Quantum Theory as an Emergent Phenomenon (1版)

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Although it is our most successful physical theory, quantum mechanics raises conceptual issues that have perplexed physicists and philosophers of science for decades. This book develops a new approach based on the proposal that quantum theory is not a complete, final theory, but, in fact, an emergent phenomenon arising from a more profound level of dynamics.

Fractional Statistics and Quantum Theory (2版)

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"As an important feature, this book contains both mathematics and physics, properly balanced for a student interested in studying theoretical physics. There are many exercises to be worked out. I am pleased to highly recommend the book for any one interested in the anyons." Professor Mukunda P Das The Australian National University Reviews of the First Edition: "This lucid monograph is highly recommended for those who want to do further research in the area as well as for those who are merely curious about this unusual aspect of quantum many-body physics." Current Science "The overall style is clear and pedagogical, with emphasis on symmetry and simplicity ... I recommend this book for newcomers, graduate students and teachers who are interested in having an introduction to the topics of the book's title." Mathematical Reviews This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced researchers with a reasonable background in quantum and statistical mechanics. Topics in the first part of the book include the flux tube model of anyons, the braid group and a detailed discussion about the various aspects of quantum and statistical mechanics of a noninteracting anyon gas. The second part of the book includes a detailed discussion about fractional statistics from the point of view of Chern-Simons theories. Topics covered here include Chern-Simons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect. Since the publication of the first edition of the book, an exciting possibility has emerged, that of quantum computing using anyons. A section has therefore been included on this topic in the second edition. In addition, new sections have been added about scattering of anyons with hard disk repulsion as well as fractional exclusion statistics and negative probabilities.

PRINCIPLES OF QUANTUM MECHANICS (2版)

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【原文書】 書名：Principles of Quantum Mechanics 2/e 作者:R. Shankar 出版社：Kluwer Academic Plenum Publishers ISBN：9780306447907 About this Textbook Reviews from the First Edition: "An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist) "No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin) Reviews of the Second Edition: "This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews) R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Consistent Quantum Theory

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This volume elucidates the consistent quantum theory approach to quantum mechanics at a level accessible to university students in physics, chemistry, mathematics, and computer science, making this an ideal supplement to standard textbooks. Griffiths provides a clear explanation of points not yet adequately treated in traditional texts and which students find confusing, as do their teachers. The book will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.

Advanced Topics in Quantum Mechanics (1版)

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Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout. Covers many advanced mathematical techniques in quantum mechanics, each illustrated with detailed examples Presents two alternative formulations of quantum mechanics; the path integral and phase space formulations, which are useful in advanced applications Provides a pedagogical and thorough overview of the exact WKB method, which plays an increasingly important role in many areas of modern physics

Advanced Topics in Finite Element Analysis of Structur with Mathematic & Matlab Computation

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【簡介】 Starting from governing differential equations, a unique and consistently weighted residual approach is used to present advanced topics in finite element analysis of structures, such as mixed and hybrid formulations, material and geometric nonlinearities, and contact problems. This book features a hands-on approach to understanding advanced concepts of the finite element method (FEM) through integrated Mathematica and MATLAB® exercises. 【目錄】 CONTENTS OF THE BOOK WEB SITE xi PREFACE xiii 1 ESSENTIAL BACKGROUND 1 1.1 Steps in a Finite Element Solution 2 1.1.1 Two-Node Uniform Bar Element 2 1.2 Interpolation Functions 12 1.2.1 Lagrange Interpolation for Second-Order Problems 14 1.2.2 Hermite Interpolation for Fourth-Order Problems 14 1.2.3 Lagrange Interpolation for Rectangular Elements 16 1.2.4 Triangular Elements 21 1.3 Integration by Parts 23 1.3.1 Gauss’s Divergence Theorem 23 1.3.2 Green-Gauss Theorem 24 1.3.3 Green-Gauss Theorem as Integration by Parts in Two Dimensions 24 1.4 Numerical Integration Using Gauss Quadrature 25 1.4.1 Gauss Quadrature for One-Dimensional Integrals 25 1.4.2 Gauss Quadrature for Area Integrals 26 1.4.3 Gauss Quadrature for Volume Integrals 28 1.5 Mapped Elements 28 1.5.1 Restrictions on Mapping of Areas 29 1.5.2 Derivatives of the Assumed Solution 30 1.5.3 Evaluation of Area Integrals 31 1.5.4 Evaluation of Boundary Integrals 32 Problems 33 2 ANALYSIS OF ELASTIC SOLIDS 37 2.1 Governing Equations 37 2.1.1 Stresses 37 2.1.2 Strains 39 2.1.3 Constitutive Equations 40 2.1.4 Temperature Effects and Initial Strains 40 2.1.5 Stress Equilibrium Equations 41 2.2 General Form of Finite Element Equations 41 2.2.1 Weak Form 41 2.2.2 Finite Element Equations 43 2.3 Tetrahedral Element 45 2.3.1 Interpolation Functions for a Tetrahedral Element 45 2.3.2 Tetrahedral Element for Three-Dimensional Elasticity 49 2.4 Mapped Solid Elements 57 2.4.1 Interpolation Functions for an Eight-Node Solid Element 58 2.4.2 Interpolation Functions for a 20-Node Solid Element 59 2.4.3 Evaluation of Derivatives 60 2.4.4 Integration over Volume 61 2.4.5 Evaluation of Surface Integrals 63 2.4.6 Evaluation of Line Integrals 67 2.4.7 Complete Mathematica MATLAB Implementations 70 2.5 Stress Calculations 77 2.5.1 Optimal Locations for Calculating Element Stresses 77 2.5.2 Interpolation-Extrapolation of Stresses 78 2.5.3 Average Nodal Stresses 79 2.5.4 Iterative Improvement in Stresses 82 2.6 Static Condensation 84 2.7 Substructuring 85 2.8 Patch Test and Incompatible Elements 90 2.8.1 Convergence Requirements 91 2.8.2 Extra Zero-Energy Modes 91 2.8.3 Patch Test for Plane Elasticity Problems 92 2.8.4 Quadrilateral Element with Additional Bending Shape Functions 98 2.9 Computer Implementation: fe2Quad 102 Problems 115 3 SOLIDS OF REVOLUTION 120 3.1 Equations of Elasticity in Cylindrical Coordinates 120 3.2 Axisymmetric Analysis 122 3.2.1 Potential Energy 123 3.2.2 Finite Element Equations 123 3.2.3 Three-Node Triangular Element 125 3.2.4 Mapped Quadrilateral Elements 146 3.3 Unsymmetrical Loading 154 3.3.1 Fourier Series Representation of Loading 154 3.3.2 Finite Element Formulation for Symmetric Loading Terms 157 3.3.3 Finite Element Formulation for Antisymmetric Loading Terms 161 Problems 166 4 MULTIFIELD FORMULATIONS FOR BEAM ELEMENTS 170 4.1 Euler-Bernoulli Beam Theory 171 4.2 Mixed Beam Element Based on EBT 173 4.3 Timoshenko Beam Theory 180 4.4 Displacement-Based Beam Element for TBT 183 4.5 Shear Locking in Displacement-Based Beam Elements for TBT 189 4.5.1 Possible Remedies for Shear Locking 190 4.6 Mixed Beam Element Based on TBT 193 4.7 Four-Field Beam Element for TBT 198 4.8 Linked Interpolation Beam Element for TBT 205 4.9 Concluding Remarks 211 Problems 212 5 MULTIFIELD FORMULATIONS FOR ANALYSIS OF ELASTIC SOLIDS 215 5.1 Governing Equations 215 5.2 Displacement Formulation 218 5.3 Stress Formulation 221 5.4 Mixed Formulation 224 5.5 Assumed Stress Field For Mixed Formulation 228 5.5.1 Minimum Number of Stress Parameters 228 5.5.2 Optimum Number of Stress Parameters 229 5.5.3 Suggested Procedure for Determining Appropriate Stress Interpolation 230 5.6 Analysis of Nearly Incompressible Solids 234 5.6.1 Deviatoric and Volumetric Stresses and Strains 236 5.6.2 Poisson Ratio Locking in the Displacement-Based Finite Elements 238 5.6.3 Mixed Formulation for Nearly Incompressible Solids 240 5.6.4 Finite Element Equations 242 5.6.5 Assumed Pressure Solution 245 5.6.6 Quadrilateral Elements for Planar Problems 246 Problems 258 6 PLATES AND SHELLS 261 6.1 Kirchhoff Plate Theory 262 6.1.1 Equilibrium Equations 266 6.1.2 Stress Computations 267 6.1.3 Weak Form for Displacement-Based Formulation 270 6.1.4 General Form of Kirchhoff Plate Element Equations 273 6.2 Rectangular Kirchhoff Plate Elements 275 6.2.1 MZC (Melosh, Zienkiewicz, and Cheung) Rectangular Plate Element 275 6.2.2 Patch Test for Plate Elements 284 6.2.3 BFS (Bogner, Fox, and Schmit) Rectangular Plate Element 291 6.3 Triangular Kirchhoff Plate Elements 299 6.3.1 BCIZ (Bazeley, Cheung, Irons, and Zienkiewicz) Triangular Plate Element 299 6.3.2 Conforming Triangular Plate Elements 305 6.4 Mixed Formulation for Kirchhoff Plates 307 6.5 Mindlin Plate Theory 311 6.6 Displacement-Based Finite Elements for Mindlin Plates 314 6.6.1 Weak Form 314 6.6.2 General Form of Mindlin Plate Element Equations 316 6.6.3 Heterosis Element 323 6.7 Multifield Elements for Mindlin Plates 325 6.8 Analysis of Shell Structures 331 6.8.1 Transformation Matrix 332 6.8.2 Transformed Equations 335 Problems 336 7 INTRODUCTION TO NONLINEAR PROBLEMS 340 7.1 Nonlinear Differential Equation 341 7.1.1 Approximate Solutions Using the Classical Form of the Galerkin Method 341 7.1.2 Finite Element Solution 344 7.2 Solution Procedures for Nonlinear Problems 353 7.2.1 Constant Stiffness Iteration 354 7.2.2 Load Increments 359 7.2.3 Arc-Length Method 365 7.3 Linearization and Directional Derivative 379 7.3.1 Examples of Linearization 380 Problems 383 8 MATERIAL NONLINEARITY 386 8.1 Analysis of Axially Loaded Bars 387 8.1.1 Weak Form 388 8.1.2 Two-Node Finite Element 389 8.1.3 One-Dimensional Plasticity 391 8.1.4 Ramberg-Osgood Model 414 8.2 Nonlinear Analysis of Trusses 424 8.3 Material Nonlinearity in General Solids 434 8.3.1 General Form of Finite Element Equations 434 8.3.2 General Formulation for Incremental Stress-Strain Equations 437 8.3.3 State Determination Procedure 440 8.3.4 von Mises Yield Criterion and the Associated Hardening Models 449 Problems 462 9 GEOMETRIC NONLINEARITY 466 9.1 Basic Continuum Mechanics Concepts 467 9.1.1 Deformation Gradient 467 9.1.2 Green-Lagrange Strains 476 9.1.3 Cauchy and Piola-Kirchhoff Stresses 481 9.2 Governing Differential Equations and Weak Forms 482 9.3 Linearization of the Weak Form 488 9.4 General Form of Element Tangent Matrices 493 9.4.1 State Determination and Check for Convergence 496 9.5 Constitutive Equations 498 9.5.1 Kirchhoff Material 498 9.5.2 Compressible Neo-Hookean Material 499 9.6 Computations For a Planar Analysis 509 9.7 Deformation-Dependent Loading 529 9.7.1 Linearized External Virtual Work for Pressure Loading: General Three-Dimensional Case 529 9.7.2 Linearized External Virtual Work for Pressure Loading: Planar Case 534 9.8 Linearized Buckling Analysis 536 9.8.1 Buckling Load for Trusses 537 9.9 Appendix: Double Contraction of Tensors 542 9.9.1 Double Contraction of Two Second-Order Tensors 542 9.9.2 Double Contraction of a Fourth-Order Tensor with a Second-Order Tensor 543 Problems 545 10 CONTACT PROBLEMS 549 10.1 Simple Normal Contact Example 549 10.1.1 Direct Solution 549 10.1.2 Solution Using Normal Contact Constraint 551 10.2 Contact Example Involving Friction 554 10.2.1 Solution of a Beam Problem with No Frictional Resistance 555 10.2.2 Frictional Constraint Function 555 10.2.3 Solution of a Beam Problem with Large Frictional Resistance 556 10.2.4 Solution of a Beam Problem with Small Frictional Resistance 557 10.3 General Contact Problems 557 10.3.1 Contact Point and Gap Calculations 558 10.3.2 Forces on the Contact Surface 564 10.3.3 Lagrange Multiplier Weak Form 565 10.3.4 Penalty Formulation 568 Problems 575 BIBLIOGRAPHY 579 INDEX 585