Quantum Mechanics
This book was written as a text, although many may consider it a mono graph. As a text it has been used several times in both the one-year graduate quantum-mechanics course and (in its shortened version) in a senior quantum mechanics course that I taught at the University of Texas at Austin. It is...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1979, 1979
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| Edition: | 1st ed. 1979 |
| Series: | Texts and Monographs in Physics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Mathematical Preliminaries
- I.1 The Mathematical Language of Quantum Mechanics
- I.2 Linear Spaces, Scalar Product
- I.3 Linear Operators, Algebras
- II Foundations of Quantum Mechanics — The Harmonic Oscillator
- II. 1 Introduction
- II.2 The First Basic Assumption of Quantum Mechanics
- II.3 Algebra of the Harmonic Oscillator
- II.4 The Relation between Experimental Data and Quantum-Mechanical Observables
- II.5 The Effect of a Measurement on the State of a Quantum-Mechanical System
- II.6 The Basic Assumptions Applied to the Harmonic Oscillator, and Some Historical Remarks
- II.7 Some General Consequences of the Basic Assumptions of Quantum Mechanics
- II.8 Eigenvectors of Position and Momentum Operators; the Wave Functions of the Harmonic Oscillator
- II.9 Comparison between Quantum and Classical Harmonic Oscillators
- II.10 Basic Assumptions II and III for Observables with Continuous Spectra
- II.11 Position and Momentum Measurements—Particles and Waves
- 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
- 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
- V.4 Parity
- 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 HydrogenSpectrum
- VII Alkali Atoms and the Schrödinger Equation of One-Electron Atoms
- 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
- 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
- XIX Time Reversal
- XIX.1 Space-Inversion Invariance and the Properties of the S-Matrix
- XIX.2 Time Reversal
- XIX.2 Appendix to Section XIX.2
- XIX.3 Time-Reversal Invariance and the Properties of the S-Matrix
- 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 Decay Rate
- XXI.5 Partial Decay Rates
- Epilogue
- XII.A Mathematical Appendix: Definitions and Properties of Operators That Depend upon a Parameter
- XIII Change of the State by Dynamical Law and by the Measuring Process — The Stern — Gerlach Experiment
- XIII.1 The Stern-Gerlach Experiment
- XIII.A Appendix
- 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
- 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 andthe Møller 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
- VII.1 The Alkali Hamiltonian and Perturbation Theory
- VII.2 Calculation of the Matrix Elements of the Operator Q?v
- VII.3 Wavefunctions and Schrödinger Equation of the Hydrogen Atom and the Alkali Atoms
- VIII Perturbation Theory
- VIII.1 Perturbation of the Discrete Spectrum
- VIII.2 Perturbation of the Continuous Spectrum—The Lippman-Schwinger Equation
- 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
- X Indistinguishable Particles
- X.1 Introduction
- 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
- XII Time Evolution
- XII.1 Time Evolution