Quantum Mechanics I

ISBN-13: 9783642838569 / Angielski / Miękka / 2012 / 417 str.

Alberto Galindo; Pseudo Pedro Pascual; J. D. Garcia

Opis

This is a textbook on non-relativistic quantum mechanics that emphasizes clarification of the nature of the basic postulates and the interpretation of the theory. It contains special material, often only accessible in scientific journals, on bound states, scattering theory, and both analytical and approximation techniques. Applications to many branches of physics are given. Among the topics covered are one-dimensional problems, angular momentum, two-particle systems, symmetry transformations, collision theory, the WKB method, and stationary and time-dependent perturbation and variational techniques. Particles in an electromagnetic field, many-body systems, atoms, and radiation theory are studied. The book is a considerably improved and completely updated English translation of a very successful Spanish textbook and is aimed at students in their second year of university.

Spis treści

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.