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pkusiyuan

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[资源] Exploring Quantum Mechanics: Galitski, 2013

Contents
Symbols used in the book xiv
Notations often used in the book xv
Universal constants xvi
1 Operators in quantum mechanics 1
1.1 Basic concepts of the theory of linear operators 2
1.2 Eigenfunctions, eigenvalues, mean values 8
1.3 The projection operators 20
1.4 Quantum-mechanical representations of operators and wave-functions;
Unitary operators 22
2 One-dimensional motion 32
2.1 Stationary states in discrete spectrum 33
2.2 The Schrödinger equation in momentum space; The Green function
and integral form of the Schr¨ odinger equation 46
2.3 The continuous spectrum; Reflection from and transmission through
potential barriers 56
2.4 Systems with several degrees of freedom; Particle in a periodic potential 74
3 Orbital angular momentum 84
3.1 General properties of angular momentum 86
3.2 Angular momentum, l = 1 94
3.3 Addition of angular momenta 99
3.4 Tensor formalism in angular momentum theory 109
4 Motion in a spherically-symmetric potential 116
4.1 Discrete spectrum states in central fields 117
4.2 Low-energy states 141
4.3 Symmetries of the Coulomb problem 153
4.4 Systems with axial symmetry 158
5 Spin 165
5.1 Spin s = 1/2 166
5.2 Spin-orbital states with spin s = 1/2; Higher spins 180
5.3 Spin density matrix; Angular distributions in decays 191
5.4 Bound states of spin-orbit-coupled particles 198
5.5 Coherent-state spin path-integral 202
xii Contents
6 Time-dependent quantum mechanics 213
6.1 The Schrödinger representation; The motion of wave packets 214
6.2 Time-dependent observables; Constants of motion 225
6.3 Time-dependent unitary transformations; The Heisenberg
picture of motion 232
6.4 The time-dependent Green function 247
6.5 Quasistationary and quasi-energy states; Berry phase 252
7 Motion in a magnetic field 270
7.1 Stationary states in a magnetic field 271
7.2 Time-dependent quantum mechanics in a magnetic field 286
7.3 Magnetic field of the orbital currents and
spin magnetic moment 291
8 Perturbation theory; Variational method; Sudden
and adiabatic theory 296
8.1 Stationary perturbation theory (discrete spectrum) 298
8.2 Variational method 316
8.3 Stationary perturbation theory (continuous spectrum) 325
8.4 Non-stationary perturbation theory; Transitions in continuous
spectrum 336
8.5 Sudden perturbations 353
8.6 Adiabatic approximation 358
9 Quasi-classical approximation; 1/N-expansion in
quantum mechanics 374
9.1 Quasi-classical energy quantization 381
9.2 Quasi-classical wavefunctions, probabilities, and mean values 408
9.3 Penetration through potential barriers 420
9.4 1/N-expansion in quantum mechanics 436
10 Identical particles; Second quantization 447
10.1 Quantum statistics; Symmetry of wavefunctions 448
10.2 Elements of the second quantization formalism
(the occupation-number representation) 456
10.3 The simplest systems with a large number of
particles (N ? 1) 472
11 Atoms and molecules 485
11.1 Stationary states of one-electron and two-electron atoms 486
11.2 Many-electron atoms; Statistical atomic model 509
11.3 Principles of two-atom-molecule theory 525
11.4 Atoms and molecules in external fields; Interaction of atomic systems 536
11.5 Non-stationary phenomena in atomic systems 565
Contents xiii
12 Atomic nucleus 598
12.1 Nuclear forces—the fundamentals; The deuteron 600
12.2 The shell model 612
12.3 Isotopic invariance 627
13 Particle collisions 637
13.1 Born approximation 642
13.2 Scattering theory: partial-wave analysis 663
13.3 Low-energy scattering; Resonant scattering 675
13.4 Scattering of fast particles; Eikonal approximation 713
13.5 Scattering of particles with spin 726
13.6 Analytic properties of the scattering amplitude 737
13.7 Scattering of composite quantum particles; Inelastic collisions 747
14 Quantum radiation theory 776
14.1 Photon emission 779
14.2 Photon scattering; Photon emission in collisions 790
15 Relativistic wave equations 810
15.1 The Klein–Gordon equation 812
15.2 The Dirac equation 838
16 Appendix 866
16.1 App.1. Integrals and integral relations 866
16.2 App.2. Cylinder functions 867
Index 871
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