Quantum mechanics / Arno Bohm

Public ISBD Titre : Quantum mechanics : Foundations and applications Type de document : texte imprimé Auteurs : Arno Bohm ; M. Loewe Mention d'édition : 3e éd. Editeur : New York : Springer-Verlag Année de publication : 1993 Importance : 1 vol (688 p.) Présentation : ill. Format : 24 cm ISBN/ISSN/EAN : 978-3-540-97944-9 Note générale : "Springer study edition" on back cover of 2001 paperback printing Catégories : Physique Mots-clés : Théorie quantique Index. décimale : 530.12 Mécanique quantique Résumé : Cette édition diffère de la deuxième par l'addition de près de 100 pages consacrées à la phase quantique (ou géométrique, ou Berry), un sujet qui n'existait pas lors de la rédaction de ce livre. Les changements dans le reste du livre consistent en des corrections d'un petit nombre de fautes d'impression. Alors qu'il peut sembler que l'ajout de deux chapitres sur la phase quantique surestime un sujet actuellement à la mode, ils complètent réellement le développement de la théorie quantique comme indiqué dans ce livre. Nous commençons avec des modèles simples, les synthétisant en "molécules" compliquées. Avec les nouveaux chapitres, nous terminons par des «molécules» compliquées, en les divisant en parties plus simples. Ce processus de division d'un système complexe en parties donne tout naturellement naissance à une théorie de jauge dont la phase géométrique est une manifestation - avec des conséquences non seulement théoriques, mais observables expérimentalement. Pour cette raison, la phase géométrique n'est pas une simple mode, mais une découverte qui conservera son importance pour toujours et qui doit être discutée dans les manuels de mécanique quantique. Je voudrais remercier Mark Loewe pour son aide et ses conseils pour l'écriture et la nouvelle partie du livre. En outre, je voudrais exprimer ma gratitude à J. Anandan, M. Berry et C.A. Mead, qui a lu des parties ou tout le nouveau matériel et ont fourni de précieux conseils. Note de contenu : Sommaire Preface to the Third Edition vii Preface to the Second Edition ix Acknowledgments xiii CHAPTER I Mathematical Preliminaries 1 1.1 The Mathematical Language of Quantum Mechanics 1 1.2 Linear Spaces, Scalar Product 2 1.3 Linear Operators 5 1.4 Basis Systems and Eigenvector Decomposition 8 1.5 Realizations of Operators and of Linear Spaces 18 1.6 Hermite Polynomials as an Example of Orthonormal Basis Functions 28 Appendix to Section 1.6 31 1.7 Continuous Functionals 33 1.8 How the Mathematical Quantities Will Be Used 39 Problems 39 CHAPTER II Foundations of Quantum Mechanics—The Harmonic Oscillator 43 II. 1 Introduction 43 11.2 The First Postulate of Quantum Mechanics 44 11.3 Algebra of the Harmonic Oscillator 50 11.4 The Relation Between Experimental Data and Quantum-Mechanical Observables 54 11.5 The Basic Assumptions Applied to the Harmonic Oscillator, and Some Historical Remarks 74 11.6 Some General Consequences of the Basic Assumptions of Quantum Mechanics 81 11.7 Eigenvectors of Position and Momentum Operators; the Wave Functions of the Harmonic Oscillator 84 xv xvi Contents 11.8 Postulates II and III for Observables with Continuous Spectra 94 11.9 Position and Momentum Measurements—Particles and Waves 101 Problems 112 CHAPTER III Energy Spectra of Some Molecules 117 ULI Transitions Between Energy Levels of Vibrating Molecules— The Limitations of the Oscillator Model 117 111.2 The Rigid Rotator 128 111.3 The Algebra of Angular Momentum 132 111.4 Rotation Spectra 138 111.5 Combination of Quantum Physical Systems—The Vibrating Rotator 146 Problems 155 CHAPTER IV Complete Systems of Commuting Observables 159 CHAPTER V Addition of Angular Momenta—The Wigner-Eckart Theorem 164 V.l Introduction—The Elementary Rotator 164 V.2 Combination of Elementary Rotators 165 V.3 Tensor Operators and the Wigner-Eckart Theorem 176 Appendix to Section V.3 181 V.4 Parity 192 Problem 204 CHAPTER VI Hydrogen Atom—The Quantum-Mechanical Kepler Problem 205 VI. 1 Introduction 20 Contents xvii CHAPTER IX Electron Spin 253 IX. 1 Introduction 253 IX.2 The Fine Structure—Qualitative Considerations 255 IX.3 Fine-Structure Interaction 261 IX.4 Fine Structure of Atomic Spectra 268 IX.5 Selection Rules 270 IX.6 Remarks on the State of an Electron in Atoms 271 Problems 272 CHAPTER X Indistinguishable Particles 274 X.l Introduction 274 Problem 281 CHAPTER XI Two-Electron Systems—The Helium Atom 282 XI. 1 The Two Antisymmetric Subspaces of the Helium Atom 282 XI.2 Discrete Energy Levels of Helium 287 XI.3 Selection Rules and Singlet-Triplet Mixing for the Helium Atom 297 XI.4 Doubly Excited States of Helium 30 3 Problems 30 9 CHAPTER XII Time Evolution 310 XII.1 Time Evolution 31 ° XII.A Mathematical Appendix: Definitions and Properties of Operators that Depend upon a Parameter 324 Problems 326 CHAPTER XIII Some Fundamental Properties of Quantum Mechanics 328 XIII. 1 Change of the State by the Dynamical Law and by the Measuring Process—The Stern-Gerlach Experiment 328 Appendix to Section XIII. 1 340 ХШ.2 Spin Correlations in a Singlet State 342 XIII.3 Bell's Inequalities, Hidden Variables, and the Einstein-PodolskyRosen Paradox 347 Problems 354 CHAPTER XIV Transitions in Quantum Physical Systems—Cross Section 356 XIV. 1 Introduction 356 XIV.2 Transition Probabilities and Transition Rates 358 XIV.3 Cross Sections 362 XIV.4 The Relation of Cross Sections to the Fundamental Physical Observables 365 XIV.5 Derivation of Cross-Section Formulas for the Scattering of a Beam off a Fixed Target 368 Problems 384 xviii Contents CHAPTER XV Formal Scattering Theory and Other Theoretical Considerations 387 XV. 1 The Lippman-Schwinger Equation 387 XV.2 In-States and Out-States 391 XV. 3 The S-Operator and the Meiler Wave Operators 399 XV.A Appendix 407 CHAPTER XVI Elastic and Inelastic Scattering for Spherically Symmetric Interactions XVI. 1 Partial-Wave Expansion XVI.2 Unitarity and Phase Shifts XVI. 3 Argand Diagrams Problems 409 409 417 422 424 CHAPTER XVII Free and Exact Radial Wave Functions 425 XVII. 1 Introduction 425 XVII.2 The Radial Wave Equation 426 XVII.3 The Free Radial Wave Function 430 XVII.4 The Exact Radial Wave Function 432 XVII.5 Poles and Bound States 439 XVII.6 Survey of Some General Properties of Scattering Amplitudes and Phase Shifts 441 XVII.A Mathematical Appendix on Analytic Functions 444 Problems 450 CHAPTER XVIII Resonance Phenomena 452 XVIII. 1 Introduction 452 XVIII.2 Time Delay and Phase Shifts 457 XVIII.3 Causality Conditions 464 XVIII.4 Causality and Analyticity 467 XVIII.5 Brief Description of the Analyticity Properties of the S-Matrix 471 XVIII.6 Resonance Scattering—Breit-Wigner Formula for Elastic Scattering 476 XVIII.7 The Physical Effect of a Virtual State 487 XVIII.8 Argand Diagrams for Elastic Resonances and Phase-Shift Analysis 489 XVIII.9 Comparison with the Observed Cross Section: The Effect of Background and Finite Energy Resolution 493 Problems 503 CHAPTER XIX Time Reversal 505 XIX. 1 Space-Inversion Invariance and the Properties of the S-Matrix 505 XIX.2 Time Reversal 507 Appendix to Section XIX.2 511 XIX.3 Time-Reversal Invariance and the Properties of the S-Matrix 512 Problems 516 Contents XIX CHAPTER XX Resonances in Multichannel Systems 517 XX. 1 Introduction 517 XX.2 Single and Double Resonances 518 XX.3 Argand Diagrams for Inelastic Resonances 532 CHAPTER XXI The Decay of Unstable Physical Systems 537 XXI. 1 Introduction 537 XXI.2 Lifetime and Decay Rate 539 XXI.3 The Description of a Decaying State and the Exponential Decay Law 542 XXI.4 Gamow Vectors and Their Association to the Resonance Poles of the S-Matrix 549 XXI.5 The Golden Rule 563 XXI.6 Partial Decay Rates 567 Problems 569 CHAPTER XXII Quantal Phase Factors and Their Consequences 571 XXII. 1 Introduction 571 XXII.2 A Quantum Physical System in a Slowly Changing Environment 573 XXII.3 A Spinning Quantum System in a Slowly Changing External Magnetic Field—The Adiabatic Approximation 587 XXII.4 A Spinning Quantum System in a Precessing External Magnetic Field—The General Cyclic Evolution 598 Problems 614 CHAPTER XXIII A Quantum Physical System in a Quantum Environment—The Gauge Theory of Molecular Physics 617 XXIII. 1 Introduction 617 XXIII.2 The Hamiltonian of the Diatomic Molecule 618 XXIII.3 The Born-Oppenheimer Method 623 XXIII.4 Gauge Theories 631 XXIII.5 The Gauge Theory of Molecular Physics 636 XXIII.6 The Electronic States of Diatomic Molecules 643 XXIII.7 The Monopole of the Diatomic Molecule 645 Problems 658 Epilogue 661 Bibliography 664 Index 669 Côte titre : Fs/0233-0234 Quantum mechanics : Foundations and applications [texte imprimé] / Arno Bohm ; M. Loewe  . -  3e éd. . - New York : Springer-Verlag, 1993 . - 1 vol (688 p.) : ill. ; 24 cm. ISBN : 978-3-540-97944-9 "Springer study edition" on back cover of 2001 paperback printing Catégories : Physique Mots-clés : Théorie quantique Index. décimale : 530.12 Mécanique quantique Résumé : Cette édition diffère de la deuxième par l'addition de près de 100 pages consacrées à la phase quantique (ou géométrique, ou Berry), un sujet qui n'existait pas lors de la rédaction de ce livre. Les changements dans le reste du livre consistent en des corrections d'un petit nombre de fautes d'impression. Alors qu'il peut sembler que l'ajout de deux chapitres sur la phase quantique surestime un sujet actuellement à la mode, ils complètent réellement le développement de la théorie quantique comme indiqué dans ce livre. Nous commençons avec des modèles simples, les synthétisant en "molécules" compliquées. Avec les nouveaux chapitres, nous terminons par des «molécules» compliquées, en les divisant en parties plus simples. Ce processus de division d'un système complexe en parties donne tout naturellement naissance à une théorie de jauge dont la phase géométrique est une manifestation - avec des conséquences non seulement théoriques, mais observables expérimentalement. Pour cette raison, la phase géométrique n'est pas une simple mode, mais une découverte qui conservera son importance pour toujours et qui doit être discutée dans les manuels de mécanique quantique. Je voudrais remercier Mark Loewe pour son aide et ses conseils pour l'écriture et la nouvelle partie du livre. En outre, je voudrais exprimer ma gratitude à J. Anandan, M. Berry et C.A. Mead, qui a lu des parties ou tout le nouveau matériel et ont fourni de précieux conseils. Note de contenu : Sommaire Preface to the Third Edition vii Preface to the Second Edition ix Acknowledgments xiii CHAPTER I Mathematical Preliminaries 1 1.1 The Mathematical Language of Quantum Mechanics 1 1.2 Linear Spaces, Scalar Product 2 1.3 Linear Operators 5 1.4 Basis Systems and Eigenvector Decomposition 8 1.5 Realizations of Operators and of Linear Spaces 18 1.6 Hermite Polynomials as an Example of Orthonormal Basis Functions 28 Appendix to Section 1.6 31 1.7 Continuous Functionals 33 1.8 How the Mathematical Quantities Will Be Used 39 Problems 39 CHAPTER II Foundations of Quantum Mechanics—The Harmonic Oscillator 43 II. 1 Introduction 43 11.2 The First Postulate of Quantum Mechanics 44 11.3 Algebra of the Harmonic Oscillator 50 11.4 The Relation Between Experimental Data and Quantum-Mechanical Observables 54 11.5 The Basic Assumptions Applied to the Harmonic Oscillator, and Some Historical Remarks 74 11.6 Some General Consequences of the Basic Assumptions of Quantum Mechanics 81 11.7 Eigenvectors of Position and Momentum Operators; the Wave Functions of the Harmonic Oscillator 84 xv xvi Contents 11.8 Postulates II and III for Observables with Continuous Spectra 94 11.9 Position and Momentum Measurements—Particles and Waves 101 Problems 112 CHAPTER III Energy Spectra of Some Molecules 117 ULI Transitions Between Energy Levels of Vibrating Molecules— The Limitations of the Oscillator Model 117 111.2 The Rigid Rotator 128 111.3 The Algebra of Angular Momentum 132 111.4 Rotation Spectra 138 111.5 Combination of Quantum Physical Systems—The Vibrating Rotator 146 Problems 155 CHAPTER IV Complete Systems of Commuting Observables 159 CHAPTER V Addition of Angular Momenta—The Wigner-Eckart Theorem 164 V.l Introduction—The Elementary Rotator 164 V.2 Combination of Elementary Rotators 165 V.3 Tensor Operators and the Wigner-Eckart Theorem 176 Appendix to Section V.3 181 V.4 Parity 192 Problem 204 CHAPTER VI Hydrogen Atom—The Quantum-Mechanical Kepler Problem 205 VI. 1 Introduction 20 Contents xvii CHAPTER IX Electron Spin 253 IX. 1 Introduction 253 IX.2 The Fine Structure—Qualitative Considerations 255 IX.3 Fine-Structure Interaction 261 IX.4 Fine Structure of Atomic Spectra 268 IX.5 Selection Rules 270 IX.6 Remarks on the State of an Electron in Atoms 271 Problems 272 CHAPTER X Indistinguishable Particles 274 X.l Introduction 274 Problem 281 CHAPTER XI Two-Electron Systems—The Helium Atom 282 XI. 1 The Two Antisymmetric Subspaces of the Helium Atom 282 XI.2 Discrete Energy Levels of Helium 287 XI.3 Selection Rules and Singlet-Triplet Mixing for the Helium Atom 297 XI.4 Doubly Excited States of Helium 30 3 Problems 30 9 CHAPTER XII Time Evolution 310 XII.1 Time Evolution 31 ° XII.A Mathematical Appendix: Definitions and Properties of Operators that Depend upon a Parameter 324 Problems 326 CHAPTER XIII Some Fundamental Properties of Quantum Mechanics 328 XIII. 1 Change of the State by the Dynamical Law and by the Measuring Process—The Stern-Gerlach Experiment 328 Appendix to Section XIII. 1 340 ХШ.2 Spin Correlations in a Singlet State 342 XIII.3 Bell's Inequalities, Hidden Variables, and the Einstein-PodolskyRosen Paradox 347 Problems 354 CHAPTER XIV Transitions in Quantum Physical Systems—Cross Section 356 XIV. 1 Introduction 356 XIV.2 Transition Probabilities and Transition Rates 358 XIV.3 Cross Sections 362 XIV.4 The Relation of Cross Sections to the Fundamental Physical Observables 365 XIV.5 Derivation of Cross-Section Formulas for the Scattering of a Beam off a Fixed Target 368 Problems 384 xviii Contents CHAPTER XV Formal Scattering Theory and Other Theoretical Considerations 387 XV. 1 The Lippman-Schwinger Equation 387 XV.2 In-States and Out-States 391 XV. 3 The S-Operator and the Meiler Wave Operators 399 XV.A Appendix 407 CHAPTER XVI Elastic and Inelastic Scattering for Spherically Symmetric Interactions XVI. 1 Partial-Wave Expansion XVI.2 Unitarity and Phase Shifts XVI. 3 Argand Diagrams Problems 409 409 417 422 424 CHAPTER XVII Free and Exact Radial Wave Functions 425 XVII. 1 Introduction 425 XVII.2 The Radial Wave Equation 426 XVII.3 The Free Radial Wave Function 430 XVII.4 The Exact Radial Wave Function 432 XVII.5 Poles and Bound States 439 XVII.6 Survey of Some General Properties of Scattering Amplitudes and Phase Shifts 441 XVII.A Mathematical Appendix on Analytic Functions 444 Problems 450 CHAPTER XVIII Resonance Phenomena 452 XVIII. 1 Introduction 452 XVIII.2 Time Delay and Phase Shifts 457 XVIII.3 Causality Conditions 464 XVIII.4 Causality and Analyticity 467 XVIII.5 Brief Description of the Analyticity Properties of the S-Matrix 471 XVIII.6 Resonance Scattering—Breit-Wigner Formula for Elastic Scattering 476 XVIII.7 The Physical Effect of a Virtual State 487 XVIII.8 Argand Diagrams for Elastic Resonances and Phase-Shift Analysis 489 XVIII.9 Comparison with the Observed Cross Section: The Effect of Background and Finite Energy Resolution 493 Problems 503 CHAPTER XIX Time Reversal 505 XIX. 1 Space-Inversion Invariance and the Properties of the S-Matrix 505 XIX.2 Time Reversal 507 Appendix to Section XIX.2 511 XIX.3 Time-Reversal Invariance and the Properties of the S-Matrix 512 Problems 516 Contents XIX CHAPTER XX Resonances in Multichannel Systems 517 XX. 1 Introduction 517 XX.2 Single and Double Resonances 518 XX.3 Argand Diagrams for Inelastic Resonances 532 CHAPTER XXI The Decay of Unstable Physical Systems 537 XXI. 1 Introduction 537 XXI.2 Lifetime and Decay Rate 539 XXI.3 The Description of a Decaying State and the Exponential Decay Law 542 XXI.4 Gamow Vectors and Their Association to the Resonance Poles of the S-Matrix 549 XXI.5 The Golden Rule 563 XXI.6 Partial Decay Rates 567 Problems 569 CHAPTER XXII Quantal Phase Factors and Their Consequences 571 XXII. 1 Introduction 571 XXII.2 A Quantum Physical System in a Slowly Changing Environment 573 XXII.3 A Spinning Quantum System in a Slowly Changing External Magnetic Field—The Adiabatic Approximation 587 XXII.4 A Spinning Quantum System in a Precessing External Magnetic Field—The General Cyclic Evolution 598 Problems 614 CHAPTER XXIII A Quantum Physical System in a Quantum Environment—The Gauge Theory of Molecular Physics 617 XXIII. 1 Introduction 617 XXIII.2 The Hamiltonian of the Diatomic Molecule 618 XXIII.3 The Born-Oppenheimer Method 623 XXIII.4 Gauge Theories 631 XXIII.5 The Gauge Theory of Molecular Physics 636 XXIII.6 The Electronic States of Diatomic Molecules 643 XXIII.7 The Monopole of the Diatomic Molecule 645 Problems 658 Epilogue 661 Bibliography 664 Index 669 Côte titre : Fs/0233-0234

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Fs/0234	Fs/0233-0234	Livre	Bibliothéque des sciences	Français	Disponible Disponible
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