Theoretical Atomic Physics

1. Review of Quantum Mechanics.- 1.1 Wave Functions and Equations of Motion.- 1.1.1 States and Wave Functions.- 1.1.2 Linear Operators and Observables.- 1.1.3 The Hamiltonian and Equations of Motion.- 1.2 Symmetries.- 1.2.1 Constants of Motion and Symmetries.- 1.2.2 The Radial Schrödinger Equation.- 1.2.3 Example: The Radially Symmetric Harmonic Oscillator.- 1.3 Bound States and Unbound States.- 1.3.1 Bound States.- 1.3.2 Unbound States.- 1.3.3 Examples.- 1.3.4 Normalization of Unbound States.- 1.4 Resonances and Channels.- 1.4.1 Channels.- 1.4.2 Feshbach Resonances.- 1.4.3 Potential Resonances.- 1.5 Methods of Approximation.- 1.5.1 Time-independent Perturbation Theory.- 1.5.2 Ritz's Variational Method.- 1.5.3 Semiclassical Approximation.- 1.6 Angular Momentum and Spin.- 1.6.1 Addition of Angular Momenta.- 1.6.2 Spin.- 1.6.3 Spin-Orbit Coupling.- Problems.- References.- 2. Atoms and Ions.- 2.1 One-Electron Systems.- 2.1.1 The Hydrogen Atom.- 2.1.2 Hydrogenic Ions.- 2.1.3 The Dirac Equation.- 2.1.4 Relativistic Corrections to the Schrödinger Equation.- 2.2 Many-Electron Systems.- 2.2.1 The Hamiltonian.- 2.2.2 Pauli Principle and Slater Determinants.- 2.2.3 The Shell Structure of Atoms.- 2.2.4 Classification of Atomic Levels.- 2.3 The N-Electron Problem.- 2.3.1 The Hartree-Fock Method.- 2.3.2 Correlations and Configuration Interaction.- 2.3.3 The Thomas-Fermi Model.- 2.3.4 Density Functional Methods.- 2.4 Electromagnetic Transitions.- 2.4.1 Transitions in General, "Golden Rule".- 2.4.2 The Electromagnetic Field.- 2.4.3 Interaction Between Atom and Field.- 2.4.4 Emission and Absorption of Photons.- 2.4.5 Selection Rules.- 2.4.6 Oscillator Strengths, Sum Rules.- Problems.- References.- 3. Atomic Spectra.- 3.1 One Electron in a Modified Coulomb Potential.- 3.1.1 Rydberg Series, Quantum Defects.- 3.1.2 Seaton's Theorem, One-Channel Quantum Defect Theory.- 3.1.3 Photoabsorption and Photoionization.- 3.2 Coupled Channels.- 3.2.1 Close-Coupling Equations.- 3.2.2 Autoionizing Resonances.- 3.2.3 Configuration Interaction, Interference of Resonances.- 3.2.4 Perturbed Rydberg Series.- 3.3 Multichannel Quantum Defect Theory (MQDT).- 3.3.1 Two Coupled Coulomb Channels.- 3.3.2 The Lu-Fano Plot.- 3.3.3 More Than Two Channels.- 3.4 Atoms in External Fields.- 3.4.1 Atoms in a Static, Homogeneous Electric Field.- 3.4.2 Atoms in a Static, Homogeneous Magnetic Field.- 3.4.3 Atoms in an Oscillating Electric Field.- Problems.- References.- 4. Simple Reactions.- 4.1 Elastic Scattering.- 4.1.1 Elastic Scattering by a Short Ranged Potential.- 4.1.2 Elastic Scattering by a Pure Coulomb Potential.- 4.1.3 Elastic Scattering by a Modified Coulomb Potential, DWBA.- 4.1.4 Feshbach Projection. Optical Potential.- 4.2 Spin and Polarization.- 4.2.1 Consequences of Spin-Orbit Coupling.- 4.2.2 Application to General Pure Spin States.- 4.2.3 Application to Mixed Spin States.- 4.3 Inelastic Scattering.- 4.3.1 General Formulation.- 4.3.2 Coupled Radial Equations.- 4.3.3 Threshold Effects.- 4.3.4 An Example.- 4.4 Exit Channels with Two Unbound Electrons.- 4.4.1 General Formulation.- 4.4.2 Application to Electrons.- 4.4.3 Example.- Problems.- References.- 5. Special Topics.- 5.1 Multiphoton Absorption.- 5.1.1 Experimental Observations on Multiphoton Ionization.- 5.1.2 Calculating Ionization Probabilities via Volkov States.- 5.1.3 Calculating Ionization Probabilities via Floquet States.- 5.2 Classical Mechanics and Quantum Mechanics.- 5.2.1 Phase Space Densities.- 5.2.2 Coherent States.- 5.2.3 Coherent Wave Packets in Real Systems.- 5.3 Chaos.- 5.3.1 Chaos in Classical Mechanics.- 5.3.2 Traces of Chaos in Quantum Mechanics.- 5.3.3 Ionization of the Hydrogen Atom in a Microwave Field.- 5.3.4 The Hydrogen Atom in a Uniform Magnetic Field.- Problems.- References.- Appendix: Special Mathematical Functions.- A.1 Legendre Polynomials, Spherical Harmonics.- A.2 Laguerre Polynomials.- A.3 Bessel Functions.- A.4 Whittaker Functions, Coulomb Functions.- References.