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Exploring Quantum Mechanics： Galitski, 2013
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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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