The Foundations of Quantum Theory

The Foundations of Quantum Theory

1st Edition - January 1, 1973

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  • Author: Sol Wieder
  • eBook ISBN: 9780323141710

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The Foundations of Quantum Theory discusses the correspondence between the classical and quantum theories through the Poisson bracket-commutator analogy. The book is organized into three parts encompassing 12 chapters that cover topics on one-and many-particle systems and relativistic quantum mechanics and field theory. The first part of the book discusses the developments that formed the basis for the old quantum theory and the use of classical mechanics to develop the theory of quantum mechanics. This part includes considerable chapters on the formal theory of quantum mechanics and the wave mechanics in one- and three-dimension, with an emphasis on Coulomb problem or the hydrogen atom. The second part deals with the interacting particles and noninteracting indistinguishable particles and the material covered is fundamental to almost all branches of physics. The third part presents the pertinent equations used to illustrate the relativistic quantum mechanics and quantum field theory. This book is of value to undergraduate physics students and to students who have background in mechanics, electricity and magnetism, and modern physics.

Table of Contents

  • Preface

    Part I One-Particle Systems

    Chapter 1. Historical Aspects

    I Black-Body Radiation

    II Characteristic Modes within a Cavity

    III The Rayleigh-Jeans (Classical) Theory

    IV Planck's (Quantum) Theory

    V The Photoelectric Effect

    VI The Compton Effect

    VII The Quantum Theory of Matter

    VIII The de Broglie Hypothesis and the Davisson-Germer Experiment

    IX The Bohr Theory of Hydrogen

    X The Correspondence Principle

    XI Summary

    Suggested Reading


    Chapter 2. Classical Mechanics

    I The Newtonian Form of Mechanics (Nonrelativistic)

    II Lagrange's Equations

    III Hamilton's Equations

    IV Poisson Brackets

    V Relativistic Dynamics

    Suggested Reading


    Chapter 3. The Formalism of Quantum Mechanics

    I Vectors in a Complex, N-Dimensional, Linear Space

    II Linear Operators

    III Eigenvalues and Eigenvectors

    IV Eigenvalue-Eigenvector Algebra for Hermitian Operators

    V The Commutator and the Eigenvalue Problem

    VI The Projection Operator

    VII The Postulates of Quantum Mechanics

    VIII Quantum Dynamics

    IX Stationary States

    X The Dimensionality of "Quantum Space"

    XI The Coordinate Representation

    XII The Transition to Wave Mechanics

    XIII The Schroedinger Wave Equation

    XIV The Schroedinger Wave Equation and Probability Flow

    Suggested Reading


    Chapter 4. Wave Mechanics in One Dimension

    I Classification of Stationary States in Wave Mechanics

    II The Free Particle in One Dimension

    III Scattering from One-Dimensional Barriers

    IV The Rectangular Barrier

    V Bound Stationary States in One Dimension

    VI The Infinite Well

    VII The Infinite Symmetric Well

    VIII Parity

    IX The Finite Symmetric Well

    X The Harmonic Oscillator

    XI Properties of Oscillator Eigenfunctions

    XII Oscillations in Nonstationary States—Classical Correspondence

    XIII The Oscillator Problem in Dirac Notation—The Ladder Method

    Suggested Reading


    Chapter 5. Wave Mechanics in Three Dimensions

    I The Eigenvalue Problem in Three Dimensions

    II The Free Particle (Cartesian Coordinates)

    III The Particle in a Box

    IV The Anisotropic Oscillator

    V Curvilinear Coordinates

    VI The Central Force Problem V=V(r)

    VII Quantization of Angular Momentum

    VIII The Free Particle (Spherical Coordinates)

    IX The Isotropic Oscillator

    X Bound States of an Attractive Coulomb Potential (V=−K/r)

    XI The Hydrogen Atom

    XII Parity and the Central Force Problem

    XIII The Effect of a Uniform Magnetic Field on the Central Force Problem

    XIV The Ladder Method

    Suggested Reading


    Chapter 6. Spin Angular Momentum

    I Pauli's Theory of Electron Spin

    II Transformation Properties of Spin Kets—The Total Angular Momentum

    III Spin and the Central Force Problem

    IV Spin Magnetism and the Spin-Orbit Interaction in Hydrogen

    V External Magnetic Fields—The Paschen-Back Effect

    Suggested Reading


    Chapter 7. Methods of Approximation

    I Perturbation Theory

    II Nondegenerate-Bound-State-Stationary Perturbation Theory (Rayleigh-Schroedinger Method)

    III An Application of the First-Order Theory

    IV Second-Order Theory

    V Perturbation of a Degenerate Level

    VI An Application of the Perturbation Theory to a Degenerate Level—The Stark Effect in Hydrogen

    VII The Hydrogen Atom with Spin-Orbit Interaction

    VIII The Anomalous Zeeman Effect in Hydrogen

    IX Time-Dependent Perturbation Theory

    X Transitions Induced by a Constant Perturbation

    XI First-Order Transitions—Fermi's Golden Rule

    XII Higher-Order Corrections to the Golden Rule

    XIII Transitions Induced by a Harmonic Perturbation

    XIV Radiative Transitions in Hydrogen

    XV Einstein's Approach to Spontaneous Emission—Detailed Balancing

    XVI The Variational (Rayleigh-Ritz) Method

    Suggested Reading


    Chapter 8. The Theory of Scattering

    I The Classical Theory of Scattering

    II The Stationary (Steady-State) Quantum Theory of Scattering

    III Rutherford Scattering (Quantum Case)

    IV A Perturbation Treatment of Stationary Scattering—The Born Series

    V The First Born Approximation

    VI Higher Born Approximations

    VII The Method of Partial Waves

    VIII The Partial Phase Shift Approximation

    IX s-Wave Scattering

    X Dynamical Quantum Scattering and Transitions

    XI Inelastic Scattering and Absorption

    Suggested Reading


    Part II Many-Particle Systems

    Chapter 9. Noninteracting Particles

    I Classical Mechanics

    II The Transition to Quantum Mechanics

    III The Coordinate Representation and Wave Mechanics

    IV The Permutation Operator

    V Distinguishable Ideal Systems

    VI Indistinguishable Ideal Systems

    VII Statistical Correlations in Ideal Bose and Fermi Systems

    VIII The "Ideal" Helium Atom

    IX Excited States in Helium

    X The Quantum Ideal Gas

    XI The N-Representation, the Density Operator, and Quantum Statistics

    Suggested Reading


    Chapter 10. Interacting Many-Particle Systems

    I The Isolated Two-Body Problem

    II Scattering from a Mobile Target

    III The Helium Atom—A Perturbation Treatment

    IV The Helium Atom—A Variational Approach

    V The Statistical Model of Thomas and Fermi for Complex Atoms

    VI The Self-Consistent Field Method and the Hartree-Fock-Slater Approximation

    VII Properties of Atoms in the HFS Approximation

    VIII Diatomic Molecules—The Adiabatic Approximation

    IX The Hydrogen Molecule and the Covalent Bond (London-Heitler Theory)

    X The Normal-Coordinate Transformation, the Linear Lattice, Phonons

    Suggested Reading


    Part III Relativistic Quantum Mechanics and Field Theory

    Chapter 11. Relativistic Quantum Mechanics

    I The Klein-Gordon Equation

    II The Dirac Equation

    III Free Dirac Particles

    IV Negative Energy States

    V A Dirac Particle in a Static Field

    VI The Dirac Particle in a Coulomb Potential—Fine Structure in Hydrogen

    Suggested Reading


    Chapter 12. Quantum Field Theory

    I Classical Theory of Fields

    II The Hamiltonian Density

    III Field Quantization

    IV Classical Electrodynamics

    V The Equivalence between Free Radiation and Oscillators

    VI Quantization of the Free Radiation (Tranverse) Field

    VII Quantum Electrodynamics—Radiative Transitions

    VIII Broadening of Spectral Lines—The Energy-Time Uncertainty Relation

    Suggested Reading


    Appendix A. The Wentzel-Kramers-Brillouin (WKB or "Phase Integral") Approximation

    Appendix B. The Heisenberg and Interaction Pictures


Product details

  • No. of pages: 415
  • Language: English
  • Copyright: © Academic Press 1973
  • Published: January 1, 1973
  • Imprint: Academic Press
  • eBook ISBN: 9780323141710

About the Author

Sol Wieder

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