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Contents of Volume I

Part 1. The formalism and its Interpretation

Chapter 1. The origins of the quantum theory

1. The end of the classical period

2. Light quanta or photons

3. Quantization of material systems

4. Correspondence principle and the old quantum theory

Chapter 2. Matter Waves and the Schrodinger Equation

1. Matter waves

2. The Schrodinger Equation

3. The time-independent Schrodinger equation

Chapter 3. One-Dimensional Quantized Systems

1. Square potentials

2. General properties of the one-dimensional Schrodinger equation

Chapter 4. Statistical Interpretation of the wave-corpuscle duality and the uncertainty relations

1. Statistical interpretation of the wave functions of wave mechanics

2. Heisenberg's uncertainty relations

3. Uncertainty relations and the measurement process

4. Description of phenomena in quantum theory. Complementarity and causality

Chapter 5. Development of the formalism of wave mechanics and its interpretation

1. Hermitean operators and physical quantities

2. Study of the discrete spectrum

3. Statistics of measurement in the general case

4. Determination of the wave function

5. Commutator algebra and its applications

Chapter 6. Classical Approximation and the WKB Method

1. The classical limit of wave mechanics

2. The WKB method

Chapter 7. General Formalism of the quantum theory: (A) Mathematical framework

1. Vectors and operators

2. Hermitean operators, projectors, and observables

3. Representation theory

Chapter 8. General Formalism: (B) Description of physical phenomena

1. Dynamical states and physical quantities

2. The equations of motion

3. Various representations of the theory

4. Quantum statistics

Part 2. Simple Systems

Chapter 9. Solution of the Schrodinger Equation by Separation of variables. Central potential

1. Particle in a central potential. General treatment

2. Central square-well potential. Free particle

3. Two-body problems. Separation of the center-of-mass motion

Chapter 10. Scattering problems. Central potential and phase-shift method

1. Cross sections and scattering amplitudes

2. Scattering by a central potential. Phase shifts

3. Potential of finite range

4. Scattering resonances

5. Various formulae and properties

Chapter 11. The Coulomb interaction

1. The hydrogen atom

2. Coulomb scattering

Chapter 12. The harmonic oscillator

1. Eigenstates and eigenvectors of the Hamiltonian

2. Applications and various properties

3. Isotropic harmonic oscillators in several dimensions

Appendix A. Distributions, sigma-"function" and Fourier transformation

Appendix B. Special functions and associated formulae

Contents of Volume II

Part 3. Symmetries and Invariance

Chapter 13. Angular momentum in quantum mechanics

1. Eigenvalues and eigenfunctions of angular momentum

2. Orbital angular momentum and the spherical harmonics

3. Angular momentum and rotations

4. Spin

5. Addition of angular momenta

6. Irreducible tensor operators

Chapter 14. Systems of identical particles. Pauli exclusion principle

1. Symmetrization postulate

2. Applications

Chapter 15. Invariance and conservation theorems. Time reversal

1. Mathematical complements. Antilinear operators

2. Transformations and groups of transformations

3. Invariance of the equations of motion and conservation laws

4. Time reversal and the principle of microreversibility

Part 4. Methods of Approximation

Chapter 16. Stationary Perturbations

1. Perturbation of a non-degenerate level

2. Perturbation of a degenerate level

3. Explicit forms for the perturbation expansion in all orders

Chapter 17. Approximate solutions of the time-dependent Schrodinger equation

1. Time dependent perturbation theory

2. Sudden or adiabatic change of the hamiltonian

Chapter 18. The variational method and associated problems

1. Variational method for bound states

2. The Hartree and Fock-Dirac atoms

3. The structure of molecules

Chapter 19. Collision theory

1. Free wave Green's function and the Born approximation

2. Generalization to distorted waves

3. Complex collisions and the Born approximation

4. Variational calculations of transition amplitudes

5. General properties of the transition matrix

Part 5. Elements of Relativistic quantum mechanics

Chapter 20. The Dirac equation

1. General Introduction

2. The Dirac and Klein-Gordon equations

3. Invariance properties of the Dirac equation

4. Interpretation of the operators and simple solutions

5. Non-relativistic limit of the Dirac equation

6. Negative energy solutions and positron theory

Chapter 21. Field quantization. Radiation theory

1. Quantization of a real scalar field

2. Coupling with an atomic system

3. Classical theory of electromagnetic radiation

4. Quantum theory of radiation

Appendix C. Vector addition coefficients and rotation matrices

Appendix D. Elements of group theory

General Index

Part 1. The formalism and its Interpretation

Chapter 1. The origins of the quantum theory

1. The end of the classical period

2. Light quanta or photons

3. Quantization of material systems

4. Correspondence principle and the old quantum theory

Chapter 2. Matter Waves and the Schrodinger Equation

1. Matter waves

2. The Schrodinger Equation

3. The time-independent Schrodinger equation

Chapter 3. One-Dimensional Quantized Systems

1. Square potentials

2. General properties of the one-dimensional Schrodinger equation

Chapter 4. Statistical Interpretation of the wave-corpuscle duality and the uncertainty relations

1. Statistical interpretation of the wave functions of wave mechanics

2. Heisenberg's uncertainty relations

3. Uncertainty relations and the measurement process

4. Description of phenomena in quantum theory. Complementarity and causality

Chapter 5. Development of the formalism of wave mechanics and its interpretation

1. Hermitean operators and physical quantities

2. Study of the discrete spectrum

3. Statistics of measurement in the general case

4. Determination of the wave function

5. Commutator algebra and its applications

Chapter 6. Classical Approximation and the WKB Method

1. The classical limit of wave mechanics

2. The WKB method

Chapter 7. General Formalism of the quantum theory: (A) Mathematical framework

1. Vectors and operators

2. Hermitean operators, projectors, and observables

3. Representation theory

Chapter 8. General Formalism: (B) Description of physical phenomena

1. Dynamical states and physical quantities

2. The equations of motion

3. Various representations of the theory

4. Quantum statistics

Part 2. Simple Systems

Chapter 9. Solution of the Schrodinger Equation by Separation of variables. Central potential

1. Particle in a central potential. General treatment

2. Central square-well potential. Free particle

3. Two-body problems. Separation of the center-of-mass motion

Chapter 10. Scattering problems. Central potential and phase-shift method

1. Cross sections and scattering amplitudes

2. Scattering by a central potential. Phase shifts

3. Potential of finite range

4. Scattering resonances

5. Various formulae and properties

Chapter 11. The Coulomb interaction

1. The hydrogen atom

2. Coulomb scattering

Chapter 12. The harmonic oscillator

1. Eigenstates and eigenvectors of the Hamiltonian

2. Applications and various properties

3. Isotropic harmonic oscillators in several dimensions

Appendix A. Distributions, sigma-"function" and Fourier transformation

Appendix B. Special functions and associated formulae

Contents of Volume II

Part 3. Symmetries and Invariance

Chapter 13. Angular momentum in quantum mechanics

1. Eigenvalues and eigenfunctions of angular momentum

2. Orbital angular momentum and the spherical harmonics

3. Angular momentum and rotations

4. Spin

5. Addition of angular momenta

6. Irreducible tensor operators

Chapter 14. Systems of identical particles. Pauli exclusion principle

1. Symmetrization postulate

2. Applications

Chapter 15. Invariance and conservation theorems. Time reversal

1. Mathematical complements. Antilinear operators

2. Transformations and groups of transformations

3. Invariance of the equations of motion and conservation laws

4. Time reversal and the principle of microreversibility

Part 4. Methods of Approximation

Chapter 16. Stationary Perturbations

1. Perturbation of a non-degenerate level

2. Perturbation of a degenerate level

3. Explicit forms for the perturbation expansion in all orders

Chapter 17. Approximate solutions of the time-dependent Schrodinger equation

1. Time dependent perturbation theory

2. Sudden or adiabatic change of the hamiltonian

Chapter 18. The variational method and associated problems

1. Variational method for bound states

2. The Hartree and Fock-Dirac atoms

3. The structure of molecules

Chapter 19. Collision theory

1. Free wave Green's function and the Born approximation

2. Generalization to distorted waves

3. Complex collisions and the Born approximation

4. Variational calculations of transition amplitudes

5. General properties of the transition matrix

Part 5. Elements of Relativistic quantum mechanics

Chapter 20. The Dirac equation

1. General Introduction

2. The Dirac and Klein-Gordon equations

3. Invariance properties of the Dirac equation

4. Interpretation of the operators and simple solutions

5. Non-relativistic limit of the Dirac equation

6. Negative energy solutions and positron theory

Chapter 21. Field quantization. Radiation theory

1. Quantization of a real scalar field

2. Coupling with an atomic system

3. Classical theory of electromagnetic radiation

4. Quantum theory of radiation

Appendix C. Vector addition coefficients and rotation matrices

Appendix D. Elements of group theory

General Index

Library of Congress subject headings for this publication: Quantum theory