The Foundations of Quantum Theory
Free Global Shipping
No minimum orderDescription
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
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
Problems
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
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
Problems
Appendix A. The Wentzel-Kramers-Brillouin (WKB or "Phase Integral") Approximation
Appendix B. The Heisenberg and Interaction Pictures
Index
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
Ratings and Reviews
There are currently no reviews for "The Foundations of Quantum Theory"