Quantum Mechanics: An Introduction / Edition 3

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Overview

The text Quantum Mechanics - An Introduction has found many friends among physics students and researchers so that the need for a third edition has arisen. There was no need for a major revision of the text but I have taken the opportunity to make several amendments and improvements. A number of misprints and minor errors have been corrected and a few clarifying remarks have been added at various places. A few figures have been added or revised, in particular the three-dimensional density plots in Chap. 9. I am grateful to several colleagues for helpful comments, in particular to Prof. R.A. King (Calgary) who supplied a comprehensive list of corrections. I also thank Dr. A. Scherdin for help with the figures and Dr. R. Mattiello who has supervised the preparation of the third edition of the book. Furthermore I acknowledge the agreeable collaboration with Dr. H. 1. Kolsch and his team at Springer-Verlag, Heidelberg.
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Editorial Reviews

Booknews
Walter Greiner Johann Wolfgang Goethe University/Frankfurt has produced a multi-volume "Theoretical Physics" which has in successive editions provided the foundation of the graduate education of a generation of German-speaking physicists. Five of those volumes Quantum mechanics--an introduction; Quantum mechanics--symmetries; Quantum mechanics--relativistic wave equations; Quantum electrodynamics; Gauge theory of weak interactions are now being made available in English translation from the 5th German edition. The present volume is in many ways redundant with some of the many fine introductory quantum texts already on the market; it treats standard topics in standard ways, but it is distinguished by the lively clarity of the exposition. Examples and exercises with detailed solutions punctuate the text. The figures are simple but adequate. The concluding chapter provides a brief review of some "conceptual and philosophical problems of quantum mechanics". Intrinsically useful, but likely to derive value mainly from its relationship to the series as a whole. NW Annotation c. Book News, Inc., Portland, OR booknews.com
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Product Details

  • ISBN-13: 9783540780458
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 10/26/2007
  • Edition description: 3rd corr. ed. 1994. 2nd printing 1997
  • Edition number: 3
  • Pages: 468
  • Product dimensions: 10.00 (w) x 7.00 (h) x 0.94 (d)

Table of Contents

1. The Quantization of Physical Quantities.- 1.1 Light Quanta.- 1.2 The Photoelectric Effect.- 1.3 The Compton Effect.- 1.4 The Ritz Combination Principle.- 1.5 The Franck-Hertz Experiment.- 1.6 The Stern-Gerlach Experiment.- 1.7 Biographical Notes.- 2. The Radiation Laws.- 2.1 A Preview of the Radiation of Bodies.- 2.2 What is Cavity Radiation?.- 2.3 The Rayleigh-Jeans Radiation Law - The Electromagnetic Eigenmodes of a Cavity.- 2.4 Planck’s Radiation Law.- 2.5 Biographical Notes.- 3. Wave Aspects of Matter.- 3.1 De Broglie Waves.- 3.2 The Diffraction of Matter Waves.- 3.3 The Statistical Interpretation of Matter Waves.- 3.4 Mean (Expectation) Values in Quantum Mechanics.- 3.5 Three Quantum Mechanical Operators.- 3.6 The Superposition Principle in Quantum Mechanics.- 3.7 The Heisenberg Uncertainty Principle.- 3.8 Biographical Notes.- 4. Mathematical Foundations of Quantum Mechanics I.- 4.1 Properties of Operators.- 4.2 Combining Two Operators.- 4.3 Bra and Ket Notation.- 4.4 Eigenvalues and Eigenfunctions.- 4.5 Measurability of Different Observables at Equal Times ....- 4.6 Position and Momentum Operators.- 4.7 Heisenberg’s Uncertainty Relations for Arbitrary Observables.- 4.8 Angular-Momentum Operators.- 4.9 Kinetic Energy.- 4.10 Total Energy.- 4.11 Biographical Notes.- 5. Mathematical Supplement.- 5.1 Eigendifferentials and the Normalization of Eigenfunctions for Continuous Spectra.- 5.2 Expansion into Eigenfunctions.- 6. The Schrödinger Equation.- 6.1 The Conservation of Particle Number in Quantum Mechanics.- 6.2 Stationary States.- 6.3 Properties of Stationary States.- 6.4 Biographical Notes.- 7. The Harmonic Oscillator.- 7.1 The Solution of the Oscillator Equation.- 7.2 The Description of the Harmonic Oscillator by Creation and Annihilation Operators.- 7.3 Properties of the Operators â and â+.- 7.4 Representation of the Oscillator Hamiltonian in Terms of â and â+.- 7.5 Interpretation of â and â+.- 7.6 Biographical Notes.- 8. The Transition from Classical to Quantum Mechanics.- 8.1 Motion of the Mean Values.- 8.2 Ehrenfest’s Theorem.- 8.3 Constants of Motion, Laws of Conservation.- 8.4 Quantization in Curvilinear Coordinates.- 8.5 Biographical Notes.- 9. Charged Particles in Magnetic Fields.- 9.1 Coupling to the Electromagnetic Field.- 9.2 The Hydrogen Atom.- 9.3 Three-Dimensional Electron Densities.- 9.4 The Spectrum of Hydrogen Atoms.- 9.5 Currents in the Hydrogen Atom.- 9.6 The Magnetic Moment.- 9.7 Hydrogen-like Atoms.- 9.8 Biographical Notes.- 10. The Mathematical Foundations of Quantum Mechanics II.- 10.1 Representation Theory.- 10.2 Representation of Operators.- 10.3 The Eigenvalue Problem.- 10.4 Unitary Transformations.- 10.5 The S Matrix.- 10.6 The Schrödinger Equation in Matrix Form.- 10.7 The Schrödinger Representation.- 10.8 The Heisenberg Representation.- 10.9 The Interaction Representation.- 10.10 Biographical Notes.- 11. Perturbation Theory.- 11.1 Stationary Perturbation Theory.- 11.2 Degeneracy.- 11.3 The Ritz Variational Method.- 11.4 Time-Dependent Perturbation Theory.- 11.5 Time-Independent Perturbation.- 11.6 Transitions Between Continuum States.- 11.7 Biographical Notes.- 12. Spin.- 12.1 Doublet Splitting.- 12.2 The Einstein-de Haas Experiment.- 12.3 The Mathematical Description of Spin.- 12.4 Wave Functions with Spin.- 12.5 The Pauli Equation.- 12.6 Biographical Notes.- 13. A Nonrelativistic Wave Equation with Spin.- 13.1 The Linearization of the Schrödinger Equation.- 13.2 Particles in an External Field and the Magnetic Moment ..- 14. Elementary Aspects of the Quantum-Mechanical Many-Body Problem.- 14.1 The Conservation of the Total Momentum of a Particle System.- 14.2 Centre-of-Mass Motion of a System of Particles in Quantum Mechanics.- 14.3 Conservation of Total Angular Momentum in a Quantum-Mechanical Many-Particle System.- 14.4 Small Oscillations in a Many-Particle System.- 14.5 Biographical Notes.- 15. Identical Particles.- 15.1 The Pauli Principle.- 15.2 Exchange Degeneracy.- 15.3 The Slater Determinant.- 15.4 Biographical Notes.- 16. The Formal Framework of Quantum Mechanics.- 16.1 The Mathematical Foundation of Quantum Mechanics - Hilbert Space.- 16.2 Operators in Hilbert Space.- 16.3 Eigenvalues and Eigenvectors.- 16.4 Operators with Continuous or Discrete-Continuous (Mixed) Spectra.- 16.5 Operator Functions.- 16.6 Unitary Transformations.- 16.7 The Direct-Product Space.- 16.8 The Axioms of Quantum Mechanics.- 16.9 Free Particles.- 16.10 A Summary of Perturbation Theory.- 17. Conceptual and Philosophical Problems of Quantum Mechanics.- 17.1 Determinism.- 17.2 Locality.- 17.3 Hidden-Variable Theories.- 17.4 Bell’s Theorem.- 17.5 Measurement Theory.- 17.6 Schrödinger’s Cat.- 17.7 Subjective Theories.- 17.8 Classical Measurements.- 17.9 The Copenhagen Interpretation.- 17.10 Indelible Recording.- 17.11 The Splitting Universe.- 17.12 The Problem of Reality.
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