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• Cover
• Foreword
• Acknowledgments
• Chapter VIII: An elementary approach to the quantum theory of scattering by a potential
• A. Introduction
• B. Stationary scattering states. Calculation of the cross section
• C. Scattering by a central potential. Method of partial waves
• COMPLEMENTS OF CHAPTER VIII, READER’S GUIDE
• Complement AVIII The free particle: stationary states with well-defined angular momentum
• 1. The radial equation
• 2. Free spherical waves
• 3. Relation between free spherical waves and plane waves
• Complement BVIII Phenomenological description of collisions with absorption
• 1. Principle involved
• 2. Calculation of the cross sections
• Complement CVIII Some simple applications of scattering theory
• 1. The Born approximation for a Yukawa potential
• 2. Low energy scattering by a hard sphere
• 3. Exercises
• Chapter IX: Electron spin
• A. Introduction of electron spin
• B. Special properties of an angular momentum 1/2
• C. Non-relativistic description of a spin 1/2 particle
• COMPLEMENTS OF CHAPTER IX, READER’S GUIDE
• Complement AIX Rotation operators for a spin 1/2 particle
• 1. Rotation operators in state space
• 2. Rotation of spin states
• 3. Rotation of two-component spinors
• Complement BIX Exercises
• Chapter X: Addition of angular momenta
• A. Introduction
• B. Addition of two spin 1/2’s. Elementary method
• C. Addition of two arbitrary angular momenta. General method
• COMPLEMENTS OF CHAPTER X, READER’S GUIDE
• Complement AX Examples of addition of angular momenta
• 1. Addition of j1 = 1 and j2 = 1
• 2. Addition of an integral orbital angular momentum and a spin 1/2
• Complement BX Clebsch-Gordan coefficients
• 1. General properties of Clebsch-Gordan coefficients
• 2. Phase conventions. Reality of Clebsch-Gordan coefficients
• 3. Some useful relations
• Complement CX Addition of spherical harmonics
• 1. The functions ΦMJ(Ω1; Ω2)
• 2. The functions Fml (Ω)
• 3. Expansion of a product of spherical harmonics; the integral of a product of three spherical harmonics
• Complement DX Vector operators: the Wigner-Eckart theorem
• 1. Definition of vector operators; examples
• 2. The Wigner-Eckart theorem for vector operators
• 3. Application: calculation of the Landé gJ factor of an atomic level
• Complement EX Electric multipole moments
• 1. Definition of multipole moments
• 2. Matrix elements of electric multipole moments
• Complement FX Two angular momenta J1 and J2 coupled by an interaction aJ1 J2
• 1. Classical review
• 2. Quantum mechanical evolution of the average values 〈J1〉 and 〈J2〉
• 3. The special case of two spin 1/2’s
• 4. Study of a simple model for the collision of two spin 1/2 particles
• Complement GX Exercises
• Chapter XI: Stationary perturbation theory
• A. Description of the method
• B. Perturbation of a non-degenerate level
• C. Perturbation of a degenerate state
• COMPLEMENTS OF CHAPTER XI, READER’S GUIDE
• Complement AXI A one-dimensional harmonic oscillator subjected to a perturbing potential in x, x2, x3
• 1. Perturbation by a linear potential
• 2. Perturbation by a quadratic potential
• 3. Perturbation by a potential in x3
• Complement BXI Interaction between the magnetic dipoles of two spin 1/2 particles
• 1. The interaction Hamiltonian W
• 2. Effects of the dipole-dipole interaction on the Zeeman sublevels of two fixed particles
• 3. Effects of the interaction in a bound state
• Complement CXI Van der Waals forces
• 1. The electrostatic interaction Hamiltonian for two hydrogen atoms
• 2. Van der Waals forces between two hydrogen atoms in the 1s ground state
• 3. Van der Waals forces between a hydrogen atom in the 1s state and a hydrogen atom in the 2p state
• 4. Interaction of a hydrogen atom in the ground state with a conducting wall
• Complement DXI The volume effect: the influence of the spatial extension of the nucleus on the atomic levels
• 1. First-order energy correction
• 2. Application to some hydrogen-like systems
• Complement EXI The variational method
• 1. Principle of the method
• 2. Application to a simple example
• 3. Discussion
• Complement FXI Energy bands of electrons in solids: a simple model
• 1. A first approach to the problem: qualitative discussion
• 2. A more precise study using a simple model
• Complement GXI A simple example of the chemical bond: the H+2 ion
• 1. Introduction
• 2. The variational calculation of the energies
• 3. Critique of the preceding model. Possible improvements 1201
• 4. Other molecular orbitals of the H+2 ion
• 5. The origin of the chemical bond; the virial theorem
• Complement HXI Exercises
• Chapter XII: An application of perturbation theory: the fine and hyperfine structure of hydrogen
• A. Introduction
• B. Additional terms in the Hamiltonian
• C. The fine structure of the n = 2 level
• D. The hyperfine structure of the n = 1 level
• E. The Zeeman effect of the 1s ground state hyperfine structure
• COMPLEMENTS OF CHAPTER XII, READER’S GUIDE
• Complement AXII The magnetic hyperfine Hamiltonian
• 1. Interaction of the electron with the scalar and vector potentials created by the proton
• 2. The detailed form of the hyperfine Hamiltonian
• 3. Conclusion: the hyperfine-structure Hamiltonian
• Complement BXII Calculation of the average values of the fine-structure Hamiltonian in the 1s, 2s and 2p states
• 1. Calculation of 〈1/R〉, 〈1/R2〉 and 〈1/R3〉
• 2. The average values 〈Wmv〉
• 3. The average values 〈WD〉
• 4. Calculation of the coefficient ξ2p associated with WSO in the 2p level
• Complement CXII The hyperfine structure and the Zeeman effect for muonium and positronium
• 1. The hyperfine structure of the 1s ground state
• 2. The Zeeman effect in the 1s ground state
• Complement DXII The influence of the electronic spin on the Zeeman effect of the hydrogen resonance line
• 1. Introduction
• 2. The Zeeman diagrams of the 1s and 2s levels
• 3. The Zeeman diagram of the 2p level
• 4. The Zeeman effect of the resonance line
• Complement EXII The Stark effect for the hydrogen atom
• 1. The Stark effect on the n = 1 level
• 2. The Stark effect on the n = 2 level
• Chapter XIII: Approximation methods for time-dependent problems
• A. Statement of the problem
• B. Approximate solution of the Schrödinger equation
• C. An important special case: a sinusoidal or constant perturbation
• D. Random perturbation
• E. Long-time behavior for a two-level atom
• COMPLEMENTS OF CHAPTER XIII, READER’S GUIDE
• Complement AXIII Interaction of an atom with an electromagnetic wave
• 1. The interaction Hamiltonian. Selection rules
• 2. Non-resonant excitation. Comparison with the elastically bound electron model
• 3. Resonant excitation. Absorption and induced emission
• Complement BXIII Linear and non-linear responses of a two-level system subject to a sinusoidal perturbation
• 1. Description of the model
• 2. The approximate solution of the Bloch equations of the system
• 3. Discussion
• 4. Exercises: applications of this complement
• Complement CXIII Oscillations of a system between two discrete states under the effect of a sinusoidal resonant perturbation
• 1. The method: secular approximation
• 2. Solution of the system of equations
• 3. Discussion
• Complement DXIII Decay of a discrete state resonantly coupled to a continuum of final states
• 1. Statement of the problem
• 2. Description of the model
• 3. Short-time approximation. Relation to first-order perturbation theory .
• 4. Another approximate method for solving the Schrödinger equation
• 5. Discussion
• Complement EXIII Time-dependent random perturbation, relaxation
• 1. Evolution of the density operator
• 2. Relaxation of an ensemble of spin 1/2’s
• 3. Conclusion
• Complement FXIII Exercises
• Chapter XIV Systems of identical particles
• A. Statement of the problem
• B. Permutation operators
• C. The symmetrization postulate
• D. Discussion
• COMPLEMENTS OF CHAPTER XIV, READER’S GUIDE
• Complement AXIV Many-electron atoms. Electronic configurations
• 1. The central-field approximation
• 2. Electron configurations of various elements
• Complement BXIV Energy levels of the helium atom. Configurations, terms, multi-plets
• 1. The central-field approximation. Configurations
• 2. The effect of the inter-electron electrostatic repulsion: exchange energy, spectral terms
• 3. Fine-structure levels; multiplets
• Complement CXIV Physical properties of an electron gas. Application to solids
• 1. Free electrons enclosed in a box
• 2. Electrons in solids
• Complement DXIV Exercises
• Appendix I: Fourier series and Fourier transforms
• 1. Fourier series
• 2. Fourier transforms
• Appendix II: The Dirac δ-”function”
• 1. Introduction; principal properties
• 2. The -”function” and the Fourier transform
• 3. Integral and derivatives of the δ-”function”
• 4. The δ-”function” in three-dimensional space
• Appendix III: Lagrangian and Hamiltonian in classical mechanics
• 1. Review of Newton’s laws
• 2. The Lagrangian and Lagrange’s equations
• 3. The classical Hamiltonian and the canonical equations
• 4. Applications of the Hamiltonian formalism
• 5. The principle of least action
• BIBLIOGRAPHY OF VOLUMES I and II
• Index [The notation (ex.) refers to an exercise]
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