# Quantum Mechanics [electronic resource] : Foundations and Applications / by Arno Böhm

- Author:
- Böhm, Arno, 1936-
- Published:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1986.
- Edition:
- 2nd ed. 1986.
- Physical Description:
- XVII, 596 pages 93 illustrations : online resource
- Additional Creators:
- SpringerLink (Online service)

##### Access Online

- Series:
- Theoretical and Mathematical Physics, 1864-5879
- Contents:
- 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 I.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 192 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 Schrödinger 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 Schrödinger Equation of the Hydrogen Atom and the Alkali Atoms -- Problem -- VIII Perturbation Theory -- VIII.I 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 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 -- 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 -- Epilogue.
- Summary:
- The first edition of this book was written as a text and has been used many times in a one-year graduate quantum mechanics course. One of the reviewers has made me aware that the book can also serve as, " . . . in principle, a handbook of nonrelativistic quantum mechanics. " In the second edition we have therefore added material to enhance its usefulness as a handbook. But it can still be used as a text if certain chapters and sections are ignored. We have also revised the original presentation, in many places at the suggestion of students or colleagues. As a consequence, the contents of the book now exceed the material that can be covered in a one-year quantum mechanics course on the graduate level. But one can easily select the material for a one-year course omitting-according to one's preference-one or several of the following sets of sections: {1. 7, XXI}, {X, XI} or just {XI}, {II. 7, XIII}, {XIV. 5, XV}, {XIX, XX}. Also the material of Sections 1. 5-1. 8 is not needed to start with the physics in Chapter II. Chapters XI, XIII, XIX, and XX are probably the easiest to dispense with and I was contemplating the deletion of some of them, but each chapter found enthusiastic supporters among the readers who advised against it. Chapter I-augmented with some applications from later chapters-can also be used as a separate introductory text on the mathematics of quantum mechanics.
- Subject(s):
- ISBN:
- 9783662011683
- Digital File Characteristics:
- PDF and text file

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