The first edition of this book was published in 1978 and a new Spanish e(,tition in 1989. When the first edition appeared, Professor A. Martin suggested that an English translation would meet with interest. Together with Professor A. S. Wightman, he tried to convince an American publisher to translate the book. Financial problems made this impossible. Later on, Professors E. H. Lieband W. Thirring proposed to entrust Springer-Verlag with the translation of our book, and Professor W. BeiglbOck accepted the plan. We are deeply grateful to all of them, since without their interest and enthusiasm this book would not have been translated. In the twelve years that have passed since the first edition was published, beautiful experiments confirming some of the basic principles of quantum me­ chanics have been carried out, and the theory has been enriched with new, im­ portant developments. Due reference to all of this has been paid in this English edition, which implies that modifications have been made to several parts of the book. Instances of these modifications are, on the one hand, the neutron interfer­ ometry experiments on wave-particle duality and the 27r rotation for fermions, and the crucial experiments of Aspect et al. with laser technology on Bell's inequalities, and, on the other hand, some recent results on level ordering in central potentials, new techniques in the analysis of anharmonic oscillators, and perturbative expansions for the Stark and Zeeman effects.

Inhalt

1. The Physical Basis of Quantum Mechanics.- 1.1 Introduction.- 1.2 The Blackbody.- 1.3 The Photoelectric Effect.- 1.4 The Compton Effect.- 1.5 Light: Particle or Wave?.- 1.6 Atomic Structure.- 1.7 The Sommerfeld-Wilson-Ishiwara (SWI) Quantization Rules.- 1.8 Fine Structure.- 1.9 The Zeeman Effect.- 1.10 Successes and Failures of the Old Quantum Theory.- 1.11 Matter Waves.- 1.12 Wave Packets.- 1.13 Uncertainty Relations.- 2. The Postulates of Quantum Mechanics.- 2.1 Introduction.- 2.2 Pure States.- 2.3 Observables.- 2.4 Results of Measurements.- 2.5 Uncertainty Relations.- 2.6 Complete Sets of Compatible Observables.- 2.7 Density Matrix.- 2.8 Preparations and Measurements.- 2.9 Schrodinger Equation.- 2.10 Stationary States and Constants of the Motion.- 2.11 The Time-Energy Uncertainty Relation.- 2.12 Quantization Rules.- 2.13 The Spectra of the Operators X and P.- 2.14 Time Evolution Pictures.- 2.15 Superselection Rules.- 3. The Wave Function.- 3.1 Introduction.- 3.2 Wave Functions.- 3.3 Position and Momentum Representations.- 3.4 Position-Momentum Uncertainty Relations.- 3.5 Probability Density and Probability Current Density.- 3.6 Ehrenfest's Theorem.- 3.7 Propagation of Wave Packets (I).- 3.8 Wave Packet Propagation (II).- 3.9 The Classical Limit of the Schrödinger Equation.- 3.10 The Virial Theorem.- 3.11 Path Integration.- 4. One-Dimensional Problems.- 4.1 Introduction.- 4.2 The Spectrum of H.- 4.3 Square Wells.- 4.4 The Harmonic Oscillator.- 4.5 Transmission and Reflection Coefficients.- 4.6 Delta Function Potentials.- 4.7 Square Potentials.- 4.8 Periodic Potentials.- 4.9 Inverse Spectral Problem.- 4.10 Mathematical Conditions.- 5. Angular Momentum.- 5.1 Introduction.- 5.2 The Definition of Angular Momentum.- 5.3 Eigenvalues of Angular Momentum Operators.- 5.4 Orbital Angular Momentum.- 5.5 Angular Momentum Uncertainty Relations.- 5.6Matrix Representations of the Rotation Operators.- 5.7 Addition of Angular Momenta.- 5.8 Clebsch-Gordan Coefficients.- 5.9 Irreducible Tensors Under Rotations.- 5.10 Helicity.- 6. Two-Particle Systems: Central Potentials.- 6.1 Introduction.- 6.2 The Radial Equation.- 6.3 Square Wells.- 6.4 The Three-Dimensional Harmonic Oscillator.- 6.5 The Hydrogen Atom.- 6.6 The Hydrogen Atom: Corrections.- 6.7 Accidental Degeneracy.- 6.8 The Hydrogen Atom: Parabolic Coordinates.- 6.9 Exactly Solvable Potentials for s-Waves.- 7. Symmetry Transformations.- 7.1 Introduction.- 7.2 Symmetry Transformations: Wigner's Theorem.- 7.3 Transformation Properties of Operators.- 7.4 Symmetry Groups.- 7.5 Space Translations.- 7.6 Rotations.- 7.7 Parity.- 7.8 Time Reversal.- 7.9 Invariances and Conservation Laws.- 7.10 Invariance Under Translations.- 7.11 Invariance Under Rotations.- 7.12 Invariance Under Parity.- 7.13 Invariance Under Time Reversal.- 7.14 Galilean Transformations.- 7.15 Isospin.- Appendix A: Special Functions.- A.1 Legendre Polynomials.- A.2 Associated Legendre Functions.- A.3 Spherical Harmonics.- A.4 Hermite Polynomials.- A.5 Laguerre Polynomials.- A.6 Generalized Laguerre Polynomials.- A.7 The Euler Gamma Function.- A.8 Bessel Functions.- A.9 Spherical Bessel Functions.- A.10 Confluent Hypergeometric Functions.- A.11 Coulomb Wave Functions.- Appendix B: Angular Momentum.- B.1 Angular Momentum.- B.2 Matrix Representation of the Rotation Operators.- B.3 Clebsch-Gordan Coefficients.- B.4 Racah Coefficients.- B.5 Irreducible Tensors.- B.6 Irreducible Vector Tensors.- B.7 Tables of Clebsch-Gordan and Racah Coefficients.- Appendix C: Summary of Operator Theory.- C.1 Notation and Basic Definitions.- C.2 Symmetric, Self-Adjoint, and Essentially Self-Adjoint Operators.- C.3 Spectral Theory of Self-Adjoint Operators.- C.4 The Spectrum of a Self-Adjoint Operator.- C.5 One-Parameter Unitary Groups.- C.6 Quadratic Forms.- C.7 Perturbation of Self-Adjoint Operators.- C.8 Perturbation of Semi-Bounded Self-Adjoint Forms.- C.9 Min-Max Principle.- C.10 Direct Integrals in Hilbert Spaces.- Appendix D: Elements of the Theory of Distributions.- D.1 Spaces of Test Functions.- D.2 Concept of a Distribution or Generalized Function.- D.3 Operations with Distributions..- D.4 Examples of Distributions.- D.5 Fourier Transformation.- Appendix E: On the Measurement Problem Quantum Mechanics.- E.1 Types of Evolution.- E.2 Sketch of a Measurement Process.- E.3 Solutions to the Dilemma.- Appendix F: Models for Hidden Variables. (A Summary.- F.1 Motivation.- F.2 Impossibility Theorems.- F.3 Hidden Variables of the First Kind and of the Second Kind (or Local Hidden Variables).- F.4 Conclusions.- Appendix G: Properties of Certain Antiunitary Operators.- G.1 Definitions and Basic Properties.- of Quantum Mechanics II.