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The Foundations of Quantum Theory
1st Edition - January 1, 1973
Author: Sol Wieder
9 7 8 - 0 - 3 2 3 - 1 4 1 7 1 - 0
The Foundations of Quantum Theory discusses the correspondence between the classical and quantum theories through the Poisson bracket-commutator analogy. The book is organized… Read more
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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.
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 Problems 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 Problems 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 Problems 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 Problems 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 Problems 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 Problems 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 Problems 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 ProblemsPart 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 Problems 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 Problems 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 Problems 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 ProblemsAppendix A. The Wentzel-Kramers-Brillouin (WKB or "Phase Integral") Approximation Appendix B. The Heisenberg and Interaction Pictures Index