1 Review of Quantum Mechanics 1
1.1 Wave Functions and Equations of Motion 1
1.1.1 States and Wave Functions 1
1.1.2 Linear Operators and Observables 3
1.1.3 The Hamiltonian and Equations of Motion 7
1.2 Symmetries 9
1.2.1 Constants of Motion and Symmetries 9
1.2.2 The Radial Schr？dinger Equation 12
1.2.3 Example:The Radially Symmetric Harmonic Oscillator 14
1.3 Bound States and Unbound States 16
1.3.1 Bound States 16
1.3.2 Unbound States 19
1.3.3 Examples 23
1.3.4 Normalization of Unbound States 28
1.4 Processes Involving Unbound States 30
1.4.1 Wave Packets 30
1.4.2 Transmission and Reflection 33
1.4.3 Time Delays and Space Shifts 35
1.5 Resonances and Channels 40
1.5.1 Channels 41
1.5.2 Feshbach Resonances 43
1.5.3 Potential Resonances 48
1.6 Methods of Approximation 50
1.6.1 Time-independent Perturbation Theory 50
1.6.2 Ritz's Variational Method 54
1.6.3 Semiclassical Approximation 57
1.6.4 Inverse Power-Law Potentials 67
1.7 Angular Momentum and Spin 72
1.7.1 Addition of Angular Momenta 74
1.7.2 Spin 75
1.7.3 Spin-Orbit Coupling 77
Problems 79
References 83
2 Atoms and Ions 85
2.1 One-Electron Systems 85
2.1.1 The Hydrogen Atom 85
2.1.2 Hydrogenic Ions 87
2.1.3 The Dirac Equation 88
2.1.4 Relativistic Corrections to the Schr？dinger Equation 93
2.2 Many-Electron Systems 95
2.2.1 The Hamiltonian 95
2.2.2 Pauli Principle and Slater Determinants 96
2.2.3 The Shell Structure of Atoms 100
2.2.4 Classification of Atomic Levels 103
2.3 The N-Electron Problem 107
2.3.1 The Hartree-Fock Method 107
2.3.2 Correlations and Configuration Interaction 112
2.3.3 The Thomas-Fermi Model 115
2.3.4 Density Functional Methods 118
2.4 Electromagnetic Transitions 120
2.4.1 Transitions in General,"Golden Rule" 121
2.4.2 The Electromagnetic Field 124
2.4.3 Interaction Between Atom and Field 129
2.4.4 Emission and Absorption of Photons 130
2.4.5 Selection Rules 135
2.4.6 Oscillator Strengths,Sum Rules 138
Problems 140
References 142
3 Atomic Spectra 145
3.1 Long-Ranged and Shorter-Ranged Potentials 146
3.1.1 Very-Long-Ranged Potentials 146
3.1.2 Shorter-Ranged Potentials 147
3.1.3 The Transition From a Finite Number to Infinitely Many Bound States,Inverse-Square Tails 152
3.1.4 Example:Truncated Dipole Series in the H- Ion 158
3.2 One Electron in a Modified Coulomb Potential 164
3.2.1 Rydberg Series,Quantum Defects 164
3.2.2 Seaton's Theorem,One-Channel Quantum Defect Theory 171
3.2.3 Photoabsorption und Photoionization 172
3.3 Coupled Channels 177
3.3.1 Close-Coupling Equations 177
3.3.2 Autoionizing Resonances 181
3.3.3 Configuration Interaction,Interference of Resonances 186
3.3.4 Perturbed Rydberg Series 191
3.4 Multichannel Quantum Defect Theory(MQDT) 193
3.4.1 Two Coupled Coulomb Channels 193
3.4.2 The Lu-Fano Plot 200
3.4.3 More Than Two Channels 203
3.5 Atoms in External Fields 211
3.5.1 Atoms in a Static,Homogeneous Electric Field 212
3.5.2 Atoms in a Static,Homogeneous Magnetic Field 219
3.5.3 Atoms in an Oscillating Electric Field 232
Problems 235
References 239
4 Simple Reactions 243
4.1 Elastic Scattering 243
4.1.1 Elastic Scattering by a Shorter-Ranged Potential 243
4.1.2 Mean Scattering Lengths 254
4.1.3 Near-Threshold Feshbach Resonances 257
4.1.4 Semiclassical Description of Elastic Scattering 259
4.1.5 Elastic Scattering by a Pure Coulomb Potential 265
4.1.6 Elastic Scattering by a Modified Coulomb Potential,DWBA 268
4.1.7 Feshbach Projection.Optical Potential 271
4.2 Spin and Polarization 273
4.2.1 Consequences of Spin-Orbit Coupling 273
4.2.2 Application to General Pure Spin States 276
4.2.3 Application to Mixed Spin States 279
4.3 Inelastic Scattering 281
4.3.1 General Formulation 281
4.3.2 Coupled Radial Equations 287
4.3.3 Threshold Effects 292
4.3.4 An Example 295
4.4 Exit Channels with Two Unbound Electrons 298
4.4.1 General Formulation 298
4.4.2 Application to Electrons 305
4.4.3 Example 309
4.4.4 Threshold Behaviour of Ionization Cross Sections 313
Problems 317
References 321
5 Special Topics 325
5.1 Multiphoton Absorption 326
5.1.1 Experimental Observations on Multiphoton Ionization 326
5.1.2 Calculating Ionization Probabilities via Volkov States 330
5.1.3 Calculating Ionization Probabilities via Floquet States 333
5.2 Classical Trajectories and Wave Packets 336
5.2.1 Phase Space Densities 337
5.2.2 Coherent States 341
5.2.3 Coherent Wave Packets in Real Systems 347
5.3 Regular and Chaotic Dynamics in Atoms 351
5.3.1 Chaos in Classical Mechanics 351
5.3.2 Traces of Chaos in Quantum Mechanics 356
5.3.3 Semiclassical Periodic Orbit Theory 363
5.3.4 Scaling Properties for Atoms in External Fields 368
5.3.5 Examples 378
5.4 Bose-Einstein Condensation in Atomic Gases 392
5.4.1 Quantum Statistics of Fermions and Bosons 392
5.4.2 The Effect of Interactions in Bose-Einstein Condensates 396
5.4.3 Realization of Bose-Einstein Condensation in Atomic Gases 400
5.5 Some Aspects of Atom Optics 402
5.5.1 Atom-Wall Interactions 404
5.5.2 Evanescent-Wave Mirrors 411
5.5.3 Quantum Reflection 416
Problems 428
References 431
A Special Mathematical Functions 439
A.1 Legendre Polynomials,Spherical Harmonics 439
A.2 Laguerre Polynomials 441
A.3 Gamma Function 442
A.4 Bessel Functions 443
A.5 Whittaker Functions,Coulomb Functions 446
References 447
Solutions to the Problems 449
References 495
Index 497