Preface Chapter 1 Background Toolkits 1.1 Prelude 1.2 Mathematical Toolkits 1.2.1 Basic skills 1.2.2 Hilbert-space algebra and Dirac notations 1.2.3 Theorems of Hermitian operators 1.3 Classical Mechanics 1.3.1 Newton's laws 1.3.2 Lagrange's and Hamilton's formalisms 1.3.3 Poisson equation of motion Chapter 2 Quantum Mechanics: Basic Principles 2.1 Wave-Particle Duality versus Momentum Operator 2.1.1 Photons versus matter waves 2.1.2 Momentum operator in coordinate representation 2.1.3 Implications of matter waves 2.1.4 Planck radiation law and Einstein coefficients 2.2 Postulations and Basic Principles 2.2.1 Schrodinger equation and postulations 2.2.2 Basic principles with wave function description 2.2.3 Uncertainty relations 2.2.4 Requirements of wave functions 2.3 Schrodinger Picture versus Heisenberg Picture 2.3.1 The Heisenberg equation of motion 2.3.2 Steady-state theorems Chapter 3 Theories of Quantum Dynamics 3.1 Hilbert-Space Dynamics Prescriptions 3.1.1 Causality and time-order exponential 3.1.2 Perturbative dynamics versus interaction picture 3.2 Density Operators and Liouville-Space Algebra 3.2.1 General properties of density operator 3.2.2 The Liouville-space descriptions 3.3 Liouville-Space Dynamics Prescriptions 3.3.1 Schrodinger picture and Heisenberg picture 3.3.2 Nonlinear response functions 3.3.3 Absorption spectrum formalism 3.4 Correlation Function Descriptions 3.4.1 Correlation functions and spectrums 3.4.2 Fluctuation-dissipation theorem 3.4.3 Fermi's golden rule for kinetic rates 3.5 Wigner Phase-Space Representation 3.5.1 Basic properties 3.5.2 Wigner representation of operator products Chapter 4 Elementary Systems 4.1 Piecewise Potential Systems 4.1.1 Quantum well: Bound-state solutions 4.1.2 Transmission and reflection problems 4.1.3 Delta-function potential systems 4.2 Simple Harmonic Oscillator Systems 4.2.1 Algebraic solutions
4.2.2 Eigenfunctions 4.3 Angular Momentum: Preliminary 4.3.1 Angular momentum along the z-direction 4.3.2 Angular momentum in three-dimensional space 4.4 Degenerate Two-Dimensional Harmonic Oscillators 4.4.1 General considerations 4.4.2 Bosonic algebra with angular momentum Chapter 5 Angular Momentum Theory and Central Force Systems 5.1 Angular Momentum Theorem 5.1.1 Basic results 5.1.2 Spin angular momentum matrices 5.2 Descriptions of Rotations and Spins 5.2.1 Rotation and spin operators 5.2.2 Spinors and Pauli matrices 5.2.3 Total angular momentum conservation 5.3 Orbital Angular Momentum Wave Functions 5.3.1 Spherical harmonics 5.3.2 Relation to Legendre functions 5.3.3 Selection rules on optical transitions 5.3.4 Rotation spectroscopy of diatomic molecules 5.4 Central Force Systems 5.4.1 Radial wave functions: General remarks 5.4.2 Spherical free-particle waves 5.4.3 Spherical harmonic oscillators 5.4.4 Onset of centrifugal potential energies Chapter 6 Hydrogenlike Atomic Systems 6.1 Atomic Orbitals and General Remarks 6.1.1 Energies and angular momentums 6.1.2 Radial wave functions 6.1.3 Empirical rules of many-electron atoms 6.2 Electromagnetic Properties of Atoms 6.2.1 Electronic current density in hydrogen atoms 6.2.2 Magnetic moment quantizations 6.3 Fine Structures of Hydrogenlike Atoms 6.3.1 Origins of fine structures 6.3.2 Relativistic kinetic energy correction 6.3.3 Spin-orbit coupling and Thomas precession 6.3.4 Final results and remarks Chapter 7 Approximation Theories and Methods 7.1 Rayleigh-Schrodinger Perturbation Theory 7.1.1 Basic setup and perturbation energies 7.1.2 Wigner's (2k + 1)-rule 7.1.3 Perturbation wave functions and remarks 7.1.4 Unified formalism and illustrations 7.2 Variation Principle Methods 7.2.1 Variation principle 7.2.2 Variation evaluation of He atoms 7.2.3 Molecular orbitals via atomic orbitals 7.3 Born-Oppenheimer Approximation Formalism 7.3.1 The Born-Oppenheimer approximation
7.3.2 Adiabatic electronic steady-state theorems 7.3.3 Nonadiabaticity considerations Chapter 8 Many-Particle Systems: Principles and Descriptions 8.1 Indistinguishable Particles Systems 8.1.1 Pauli exclusion principle 8.1.2 Slater determinant: Noninteracting nature 8.1.3 Spin properties of Slater determinants 8.2 Second Quantization Formalism 8.2.1 Fermionic Fock-space descriptions 8.2.2 Dynamic operators in second quantization Chapter 9 Symmetry-Adapted Wave Functions 9.1 Diatomic Molecules and Spectroscopic Terms 9.1.1 Symmetry-adapted molecular orbitals 9.1.2 Configurations and spectroscopic terms 9.2 Group Representation Theories 9.2.1 Mathematical group descriptions 9.2.2 Theory of irreducible representations 9.2.3 Direct product and decompositions 9.2.4 Molecular symmetry group descriptions 9.3 Symmetry Analysis of Normal Vibrations 9.3.1 Symmetry aspects of vibrations 9.3.2 Symmetry-adapted normal modes 9.4 Symmetry Aspects of Electronic Structures 9.4.1 Revisits of diatomic molecules 9.4.2 Principles of term-symbol description 9.4.3 Conformers of H3 molecule and remarks Chapter 10 Determinantal Mean-Field Theory 10.1 Energetics of Determinantal Wave Function 10.1.1 Coulomb integral and exchange integral 10.1.2 Correlation integral and Hamiltonian matrix 10.2 The Hartree-Fock Theory 10.2.1 Single-particle mean-field description 10.2.2 Canonical Hartree-Fock equation 10.3 The Spatial Orbitals Formalism 10.3.1 Spin-unrestricted Pople-Nesbet equation 10.3.2 Spin-restricted Roothaan equation 10.3.3 Atomic orbitals in molecules and computations 10.4 Illustrations: Minimal Basis H2 Molecule 10.4.1 Restricted Hartree-Fock solutions 10.4.2 Unrestricted Hartree-Fock solutions 10.4.3 Exact solutions with correlation 10.4.4 Nuclear-spin isomers: Ortho-H2 and para-H2 Chapter 11 Many-Electron Wave Function Theories 11.1 Configuration-Space Formulations 11.1.1 Basic relations 11.1.2 Configuration interaction theory 11.1.3 Many-body perturbation theory 11.2 Coupled Cluster Wave Function Theory 11.2.1 Coupled cluster formalism 11.2.2 Onset of coupled cluster doubles
11.2.3 Some useful remarks Chapter 12 Reduced Descriptions and Density Functional Theory 12.1 Reduced Density Operator Descriptions 12.1.1 Energy aspect of many-electron systems 12.1.2 Exchange-correlation formalism 12.1.3 Reduced density matrices formalisms 12.2 Density Functional Theory and Related Issues 12.2.1 Hohenberg-Kohn theorems 12.2.2 Issues of representability 12.2.3 Onsets of density function descriptions 12.2.4 Thomas-Fermi and related models 12.3 Kohn-Sham Density Functional Theory 12.3.1 Kohn-Sham orbitals 12.3.2 Related formulations and elaborations 12.3.3 Concluding remarks Review and Assessment
[