理论原子物理学

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 Harniltonian and Equations of Motion

1.2 Symmetries

1.2.1 Constants of Motion and Symmetries

1.2.2 The Radial SchrSdinger 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 Processes Involving Unbound States

1.4.1 Wave Packets

1.4.2 Transmission and Reflection

1.4.3 Time Delays and Space Shifts

1.5 Resonances and Channels

1.5.1 Channels

1.5.2 Feshbach Resonances

1.5.3 Potential Resonances

1.6 Methods of Approximation

1.6.1 Time-independent Perturbation Theory

1.6.2 Ritzs Variational Method

1.6.3 Semiclassical Approximation

1.6.4 Inverse Power-Law Potentials

1.7 Angular Momentum and Spin

1.7.1 Addition of Angular Momenta

1.7.2 Spin

1.7.3 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 Schrodinger 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 Long-Ranged and Shorter-Ranged Potentials

3.1.1 Very-Long-Ranged Potentials

3.1.2 Shorter-Ranged Potentials

3.1.3 The Transition From a Finite Number to Infinitely Many Bound States， Inverse-Square Tails

3.1.4 Example： Truncated Dipole Series in the H- Ion

3.2 One Electron in a Modified Coulomb Potential

3.2.1 Rydberg Series， Quantum Defects

3.2.2 Seatons Theorem， One-Channel Quantum Defect. Theory

3.2.3 Photoabsorption und Photoionization

3.3 Coupled Channels

3.3.1 Close-Coupling Equations

3.3.2 Autoionizing Resonances

3.3.3 Configuration Interaction， Interference of Resonances

3.3.4 Perturbed Rydberg Series

3.4 Multichannel Quantum Defect Theory （MQDT）

3.4.1 Two Coupled Coulomb Channels

3.4.2 The Lu-Fano Plot

3.4.3 More Than Two Channels

3.5 Atoms in External Fields

3.5.1 Atoms in a Static， Homogeneous Electric Field

3.5.2 Atoms in a Static， Homogeneous Magnetic Field

3.5.3 Atoms in an Oscillating Electric Field

Problems

References

4 Simple Reactions

4.1 Elastic Scattering

4.1.1 Elastic Scattering by a Shorter-Ranged Potential

411.2 Mean Scattering Lengths

4.1.3 Near-Threshold Feshbach Resonances

4.1.4 Semiclassical Description of Elastic Scattering

4.1.5 Elastic Scattering by a Pure Coulomb Potential

4.1.6 Elastic Scattering by a Modified Coulomb Potential， DWBA

4.1.7 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

4.4.4 Threshold Behaviour of Ionization Cross Sections

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 Trajectories and Wave Packets

5.2.1 Phase Space Densities

5.2.2 Coherent States

5.2.3 Coherent Wave Packets in Real Systems

5.3 Regular and Chaotic Dynamics in Atoms

5.3.1 Chaos in Classical Mechanics

5.3.2 Traces of Chaos in Quantum Mechanics

5.3.3 Semiclassical Periodic Orbit Theory

5.3.4 Scaling Properties for Atoms in External Fields

5.3.5 Examples

5.4 Bose-Einstein Condensation in Atomic Gases

5.4.1 Quantum Statistics of Fermions and Bosons

5.4.2 The Effect of Interactions in Bose-Einstein Condensates

5.4.3 Realization of Bose-Einstein Condensation in Atomic Gases

5.5 Some Aspects of Atom Optics

5.5.1 Atom-Wall Interactions

5.5.2 Evanescent-Wave Mirrors

5.5.3 Quantum Reflection

Problems

References

A Special Mathematical Functions

A.1 Legendre Polynomials， Spherical Harmonics

A.2 Laguerre Polynomials

A.3 Gamma Function

A.4 Bessel Functions

A.5 Whittaker Functions， Coulomb Functions

References

Solutions to the Problems

References

Index

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