Introduction to the Quantum World of Atoms and Molecules

by DAHL JENS PEDER

• ISBN13: 9789810245658
• ISBN10: 9810245653
• Format: Hardcover
• Copyright: 2001-06-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Introduction to the quantum world of atoms and molecules, offering a careful development of the underlying basis of quantum mechanics. Pays special attention to exposing and clarifying the common ground of Hartree-Fock theory and density-functional theory. Includes end-of-chapter exercises.

Table of Contents

Preface	v
The Rise of Atomic Theory	1	(19)
Early Atomic Theories	2	(1)
The Chemical Atom	3	(1)
The Kinetic Molecule	4	(3)
The Spectroscopic Atom	7	(2)
Antiatomism	9	(1)
The Discovery of the Electron. The Planetary Atom	10	(3)
The Constituents of Atoms and Molecules. The Modern View	13	(3)
External Interactions. Photons	16	(4)
The Birth of Quantum Mechanics	20	(30)
Black-Body Radiation and Planck's Discovery	21	(6)
Photons and the Photoelectric Effect	27	(4)
The Photon is a Relativistic Particle	31	(2)
The Heat-Capacity Problem	33	(4)
Bohr's Theory of the Hydrogen Atom	37	(6)
De Broglie Waves	43	(7)
Wave Mechanics	50	(11)
The Time-Dependent Schrodinger Equation	51	(3)
The Time-Independent Schrodinger Equation	54	(1)
Schrodinger Operators	55	(2)
The Statistical Interpretation	57	(4)
Particle in a Box	61	(32)
Introduction	62	(3)
The One-Dimensional Box	65	(5)
Orthogonality of Wavefunctions	70	(2)
Number of Nodes Versus Energy	72	(1)
Inversion Symmetry	72	(3)
The Three-Dimensional Box	75	(1)
The Concept of Degeneracy	76	(6)
The Free-Electron Model	82	(5)
Non-Stationary States	87	(6)
Quantum-Mechanical Operators	93	(40)
The Bra-Ket Notation	94	(3)
Linear Operators. The Commutator	97	(4)
Hermitian Operators. Hermitian Conjugation	101	(6)
Some Properties of Hermitian Operators	107	(4)
Expectation Values and Uncertainties	111	(3)
The Particle in a Box Revisited	114	(3)
Commuting Hermitian Operators	117	(3)
The General Uncertainty Principle	120	(1)
Quantum Theory and Measurements	121	(4)
Matrix Algebra	125	(8)
The Free Particle	133	(14)
The Stationary States of the Free Particle	134	(5)
Non-Stationary States of the Free Particle	139	(4)
The Gaussian Wave Packet	143	(2)
From One to Three Dimensions	145	(2)
The Harmonic Oscillator	147	(18)
Definitions	148	(1)
The Schrodinger Equation for the Harmonic Oscillator	149	(2)
Solving the Schrodinger Equation	151	(4)
The Wavefunctions	155	(3)
The Algebraic Method	158	(7)
The Central Field Problem	165	(27)
The Reduced Mass of a Two-Body System	167	(4)
Spherical Polar Coordinates	171	(3)
Spherical Harmonics	174	(12)
The Dimensionless Angular-Momentum Operators	175	(1)
Looking for Common Eigenfunctions of l2 and lz	176	(2)
The Raising and Lowering Operators	178	(2)
The Quantum Number l	180	(1)
A Phase Convention	181	(2)
The Analytical Expressions	183	(3)
The Radial Function P(r)	186	(6)
The Hydrogen Atom	192	(26)
The Effective Potential. General Notation	193	(2)
The Radial Equation for the Hydrogen-Like Atom	195	(6)
The Normalized Radial Functions	201	(2)
Radial Probability Densities	203	(5)
The Complete Wavefunctions	208	(10)
The Spinning Electron	218	(28)
General Angular Momentum Theory	220	(2)
Spin, Spin Functions and Spin-Orbitals	222	(4)
Properties of the Spin One-Half Operators	226	(4)
The One-Electron Atom in External Fields	230	(9)
The Hamiltonian With Spin Neglected	230	(2)
The Hamiltonian With Spin Included	232	(2)
The Refined Hamiltonian	234	(5)
The Zeeman Effect	239	(2)
The Pauli Equation	241	(1)
Angular-Momentum Theory and Rotations	242	(4)
The Periodic Table by Electron Counting	246	(24)
The Many-Electron Atom	247	(2)
Neglect of Electron-Electron Repulsion	249	(3)
The Aufbau Principle	252	(2)
Exchange Degeneracy	254	(3)
Pauli's Exclusion Principle. Slater Determinants	257	(3)
Including Electron-Electron Repulsion	260	(1)
Slater Type Orbitals	261	(9)
The Variational Method	270	(19)
Introduction	270	(1)
Variational Principles	271	(1)
The Time-Independent Schrodinger Equation	272	(2)
The Variational Method	274	(5)
The Linear Variational Method	279	(4)
Factorization of Secular Problems	283	(6)
Diatomic Molecules	289	(35)
The Adiabatic Approximation	290	(5)
One-Electron Diatomic Molecules	295	(8)
The LCAO Approximation	303	(2)
The Homonuclear Case. Ground State of H2+	305	(9)
LCAO-MOs for Homonuclear Diatomics	314	(4)
Electronic Structure of Homonuclear Diatomics	318	(6)
Vibration and Rotation of Diatomic Molecules	324	(17)
Introduction	324	(2)
The Vibrational Motion	326	(8)
The Vibrating Rotator	334	(4)
On Rotational and Vibrational Spectra	338	(3)
Atomic Term Symbols	341	(26)
Orthonormal Bases and Unitary Matrices	342	(3)
Coupling of Two Angular Momenta	345	(6)
The Uncoupled Representation	345	(3)
The Coupled Representation	348	(3)
Vector-Coupling Coefficients by the Construction Method	351	(5)
Coupling of Two Spin 1/2 Particles	353	(2)
Coupling of Spin and Orbital Angular Momentum	355	(1)
Angular Momenta in Many-Electron Atoms	356	(11)
The Total Orbital Angular Momentum	357	(1)
The Total Spin Angular Momentum	358	(2)
L-S Coupling	360	(2)
Adding the Nuclear Angular Momentum. Bose-Einstein Condensates	362	(5)
Atomic Terms. Wavefunctions and Energies	367	(21)
Operating on Slater Determinants	368	(2)
Term Wavefunctions	370	(4)
The Helium Atom	370	(3)
The Carbon Atom	373	(1)
Matrix Elements Between Slater Determinants	374	(6)
Energies of Atomic Terms	380	(5)
The Helium Atom	382	(1)
The Beryllium Atom	383	(1)
The Carbon Atom	384	(1)
Hund's Rules	385	(3)
Electronic Terms of Diatomic Molecules	388	(8)
The Oxygen Molecule. Term Analysis	388	(3)
The Oxygen Molecule. Real Wavefunctions	391	(1)
The Oxygen Molecule. Term Energies	392	(4)
The Hartree-Fock Method	396	(16)
Hartree-Fock Method for a Single Determinant	397	(7)
Spin Restrictions	404	(3)
Conventional Hartree-Fock Theory	407	(3)
The Correlation Problem	410	(2)
Density-Functional Theory	412	(14)
Reduced Density Matrices	413	(4)
Single Slater Determinant	417	(3)
The Hohenberg-Kohn Theorem	420	(2)
The Kohn-Sham Equations	422	(4)
A Complex Numbers and Quantum Mechanics	426	(3)
B Atomic Units	429	(5)
The International System of Units (SI)	429	(1)
Atomic Units	430	(4)
C Curvilinear Coordinate Systems	434	(6)
D Surface Spherical Harmonics and Special Functions	440	(2)
E The δ-Function	442	(9)
Index	451