Quantum Mechanics : Foundations and Applications
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書誌事項
Quantum Mechanics : Foundations and Applications
（Texts and monographs in physics）
Springer-Verlag, 2001
3rd ed., rev. and enl. / prepared with Mark Loewe
- pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This edition differs from the second chiefly in the addition of about tOO pages devoted to the quantum (or geometric, or Berry) phase, a subject that did not exist when this book was written. The changes in the remainder of the book consist of corrections of a small number of misprints. While it may seem that adding two chapters on the quantum phase is overemphasizing a currently fashionable subject, they actually complete the development of quantum theory as given in this book. We start with simple models, synthesizing them into complicated "molecules." With the new chap ters, we end with complicated "molecules," dividing them into simpler parts. This process of dividing a complex system into parts quite naturally gives rise to a gauge theory, of which the geometric phase is a manifestation - with consequences not only in theory, but observable in experiments. For this rea son, the geometric phase is not a mere fashion, but a discovery that will retain its importance forever and must be discussed in textbooks on quantum mechanics. I would like to acknowledge help and advice from Mark Loewe with the writing and also of the new part of the book. In addition, I would like to express my gratitude to J. Anandan, M. Berry, and C.A. Mead, who have read parts or all of the new material and have provided valuable advice.
目次
- I Mathematical Preliminaries.- I.1 The Mathematical Language of Quantum Mechanics.- I.2 Linear Spaces, Scalar Product.- I.3 Linear Operators.- I.4 Basis Systems and Eigenvector Decomposition.- I.5 Realizations of Operators and of Linear Spaces.- I.6 Hermite Polynomials as an Example of Orthonormal Basis Functions.- Appendix to Section 1.6.- I.7 Continuous Functionals.- I.8 How the Mathematical Quantities Will Be Used.- Problems.- II Foundations of Quantum Mechanics-The Harmonic Oscillator.- II.1 Introduction.- II.2 The First Postulate of Quantum Mechanics.- II.3 Algebra of the Harmonic Oscillator.- II.4 The Relation Between Experimental Data and Quantum-Mechanical Observables.- II.5 The Basic Assumptions Applied to the Harmonic Oscillator, and Some Historical Remarks.- II.6 Some General Consequences of the Basic Assumptions of Quantum Mechanics.- II.7 Eigenvectors of Position and Momentum Operators
- the Wave Functions of the Harmonic Oscillator.- II.8 Postulates II and III for Observables with Continuous Spectra.- II.9 Position and Momentum Measurements-Particles and Waves.- Problems.- III Energy Spectra of Some Molecules.- III.1 Transitions Between Energy Levels of Vibrating Molecules-The Limitations of the Oscillator Model.- III.2 The Rigid Rotator.- III.3 The Algebra of Angular Momentum.- III.4 Rotation Spectra.- III.5 Combination of Quantum Physical Systems-The Vibrating Rotator.- Problems.- IV Complete Systems of Commuting Observables.- V Addition of Angular Momenta-The Wigner-Eckart Theorem.- V.1 Introduction-The Elementary Rotator.- V.2 Combination of Elementary Rotators.- V.3 Tensor Operators and the Wigner-Eckart Theorem.- Appendix to Section V.3.- V.4 Parity.- Problem.- VI Hydrogen Atom-The Quantum-Mechanical Kepler Problem.- VI.1 Introduction.- VI.2 Classical Kepler Problem.- VI.3 Quantum-Mechanical Kepler Problem.- VI.4 Properties of the Algebra of Angular Momentum and the Lenz Vector.- VI.5 The Hydrogen Spectrum.- Problem.- VII Alkali Atoms and the Schroedinger Equation of One-Electron Atoms.- VII.1 The Alkali Hamiltonian and Perturbation Theory.- VII.2 Calculation of the Matrix Elements of the Operator Q-?.- VII.3 Wave Functions and Schroedinger Equation of the Hydrogen Atom and the Alkali Atoms.- Problem.- VIII Perturbation Theory.- VIII.1 Perturbation of the Discrete Spectrum.- VIII.2 Perturbation of the Continuous Spectrum-The Lippman-Schwinger Equation.- Problems.- IX Electron Spin.- IX.1 Introduction.- IX.2 The Fine Structure-Qualitative Considerations.- IX.3 Fine-Structure Interaction.- IX.4 Fine Structure of Atomic Spectra.- IX.5 Selection Rules.- IX.6 Remarks on the State of an Electron in Atoms.- Problems.- X Indistinguishable Particles.- X.1 Introduction.- Problem.- XI Two-Electron Systems-The Helium Atom.- XI.1 The Two Antisymmetric Subspaces of the Helium Atom.- XI.2 Discrete Energy Levels of Helium.- XI.3 Selection Rules and Singlet-Triplet Mixing for the Helium Atom.- XI.4 Doubly Excited States of Helium.- Problems.- XII Time Evolution.- XII.1 Time Evolution.- XII.A Mathematical Appendix: Definitions and Properties of Operators that Depend upon a Parameter.- Problems.- XIII Some Fundamental Properties of Quantum Mechanics.- XIII.1 Change of the State by the Dynamical Law and by the Measuring Process-The Stern-Gerlach Experiment.- Appendix to Section XIII.1.- XIII.2 Spin Correlations in a Singlet State.- XIII.3 Bell's Inequalities, Hidden Variables, and the Einstein-Podolsky-Rosen Paradox.- Problems.- XIV Transitions in Quantum Physical Systems-Cross Section.- XIV.1 Introduction.- XIV.2 Transition Probabilities and Transition Rates.- XIV.3 Cross Sections.- XIV.4 The Relation of Cross Sections to the Fundamental Physical Observables.- XIV.5 Derivation of Cross-Section Formulas for the Scattering of a Beam off a Fixed Target.- Problems.- XV Formal Scattering Theory and Other Theoretical Considerations.- XV.1 The Lippman-Schwinger Equation.- XV.2 In-States and Out-States.- XV.3 The S-Operator and the Moller Wave Operators.- XV.A Appendix.- 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.- XVII Free and Exact Radial Wave Functions.- XVII.1 Introduction.- XVII.2 The Radial Wave Equation.- XVII.3 The Free Radial Wave Function.- XVII.4 The Exact Radial Wave Function.- XVII.5 Poles and Bound States.- XVII.6 Survey of Some General Properties of Scattering Amplitudes and Phase Shifts.- XVII.A Mathematical Appendix on Analytic Functions.- Problems.- XVIII Resonance Phenomena.- XVIII.1 Introduction.- XVIII.2 Time Delay and Phase Shifts.- XVIII.3 Causality Conditions.- XVIII.4 Causality and Analyticity.- XVIII.5 Brief Description of the Analyticity Properties of the S-Matrix.- XVIII.6 Resonance Scattering-Breit-Wigner Formula for Elastic Scattering.- XVIII.7 The Physical Effect of a Virtual State.- XVIII.8 Argand Diagrams for Elastic Resonances and Phase-Shift Analysis.- XVIII.9 Comparison with the Observed Cross Section: The Effect of Background and Finite Energy Resolution.- Problems.- XIX Time Reversal.- XIX.1 Space-Inversion Invariance and the Properties of the S-Matrix.- XIX.2 Time Reversal.- Appendix to Section XIX.2.- XIX.3 Time-Reversal Invariance and the Properties of the S-Matrix.- Problems.- XX Resonances in Multichannel Systems.- XX.1 Introduction.- XX.2 Single and Double Resonances.- XX.3 Argand Diagrams for Inelastic Resonances.- XXI The Decay of Unstable Physical Systems.- XXI.1 Introduction.- XXI.2 Lifetime and Decay Rate.- XXI.3 The Description of a Decaying State and the Exponential Decay Law.- XXI.4 Gamow Vectors and Their Association to the Resonance Poles of the S-Matrix.- XXI.5 The Golden Rule.- XXI.6 Partial Decay Rates.- Problems.- XXII Quantal Phase Factors and Their Consequences.- XXII.1 Introduction.- XXII.2 A Quantum Physical System in a Slowly Changing Environment.- XXII.3 A Spinning Quantum System in a Slowly Changing External Magnetic Field-The Adiabatic Approximation.- XXII.4 A Spinning Quantum System in a Processing External Magnetic Field-The General Cyclic Evolution.- Problems.- XXIII A Quantum Physical System in a Quantum Environment-The Gauge Theory of Molecular Physics.- XXIII.1 Introduction.- XXIII.2 The Hamiltonian of the Diatomic Molecule.- XXIII.3 The Born-Oppenheimer Method.- XXIII.4 Gauge Theories.- XXIII.5 The Gauge Theory of Molecular Physics.- XXIII.6 The Electronic States of Diatomic Molecules.- XXIII.7 The Monopole of the Diatomic Molecule.- Problems.- Epilogue.
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