Atoms and Molecules

Atoms and Molecules

by Mitchel Weissbluth

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Overview

Atoms and Molecules by Mitchel Weissbluth

Atoms and Molecules describes the basic properties of atoms and molecules in terms of group theoretical methods in atomic and molecular physics. The book reviews mathematical concepts related to angular momentum properties, finite and continuous rotation groups, tensor operators, the Wigner-Eckart theorem, vector fields, and vector spherical harmonics. The text also explains quantum mechanics, including symmetry considerations, second quantization, density matrices, time-dependent, and time-independent approximation methods. The book explains atomic structure, particularly the Dirac equation in which its nonrelativistic approximation provides the basis for the derivation of the Hamiltonians for all important interactions, such as spin-orbit, external fields, hyperfine. Along with multielectron atoms, the text discusses multiplet theory, the Hartree-Fock formulation, as well as the electromagnetic radiation fields, their interactions with atoms in first and higher orders. The book explores molecules and complexes, including the Born-Oppenheimer approximation, molecular orbitals, the self-consistent field method, electronic states, vibrational and rotational states, molecular spectra, and the ligand field theory. The book can prove useful for graduate or advanced students and academicians in the field of general and applied physics.

Product Details

ISBN-13: 9780323142946
Publisher: Elsevier Science
Publication date: 12/02/2012
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 730
File size: 25 MB
Note: This product may take a few minutes to download.

Table of Contents

Preface


Part I Mathematical Background


Chapter 1 Angular Momentum


1.1 Orbital Angular Momentum


1.2 Spherical Harmonics and Related Functions


1.3 Generalized Angular Momentum


1.4 Spin


1.5 Coupling of Two Angular Momenta


1.6 Coupling of Three Angular Momenta


1.7 Summary and Examples


Chapter 2 Rotations


2.1 Coordinate Rotations and Scalar Functions


2.2 Rotations and Angular Momenta


2.3 Transformation Properties of Angular Momentum Eigenfunctions


Chapter 3 Elements of Group Theory


3.1 Definitions and Basic Properties


3.2 Representations and Characters


3.3 Reducible and Irreducible Representations


3.4 Basis Functions


3.5 Projection Operators


3.6 Product Representations


3.7 Matrix Elements


Chapter 4 Continuous Rotation Groups


4.1 Rotation Group in Two Dimensions, C∞


4.2 Rotation Group in Three Dimensions, 0+(3)


4.3 Special Unitary Group in Two Dimensions, SU(2)


4.4 Connection between 0+(3) and SU(2)


4.5 Irreducible Representations of 0+(3)


4.6 Summary and Examples


Chapter 5 Finite Groups


5.1 Point Groups—Symmetry Operations and Nomenclature


5.2 Double Groups


5.3 The Groups 0, D4 and D6h


5.4 Permutation Groups Sn — Young Diagrams


Chapter 6 Tensors


6.1 Irreducible Tensor Operators


6.2 Tensor Products


6.3 Wigner-Eckart Theorem


6.4 Cartesian Tensors


6.5 Tensors, Permutation Groups, Continuous Groups


Chapter 7 Vector Fields


7.1 Rotational Properties


7.2 Vector Spherical Harmonics


7.3 Plane Wave Expansion


7.4 Multipole Expansion of the Electromagnetic Field


Part II Quantum-Mechanical Background


Chapter 8 Symmetry Elements of the Hamiltonian


8.1 Connection Between Group Theory and Quantum Mechanics


8.2 Geometrical Symmetries


8.3 Time Reversal and Kramers' Theorem


8.4 Indistinguishability of Particles


Chapter 9 Time Development of a Quantum Syste


9.1 Schrödinger Representation


9.2 Heisenberg Representation


9.3 Interaction Representation


9.4 Infinite Limits


Chapter 10 Harmonic Oscillator


10.1 Schrödinger Solutions


10.2 Matrix Formulation


10.3 Heisenberg Representation


Chapter 11 Slater Determinants


11.1 Matrix Elements—General


11.2 Matrix Elements—Special Cases


Chapter 12 Second Quantization


12.1 Creation and Annihilation Operators


12.2 Matrix Elements of Operators


12.3 Diagrams


12.4 Field Operators


Chapter 13 Density Matrices


13.1 General Properties


13.2 Spin States


13.3 Reduced Density Matrices


13.4 Thermal Equilibrium


13.5 Equation of Motion


13.6 Multielectron Systems


13.7 Fock-Dirac Density Matrices


13.8 Spinless Density Matrices


Chapter 14 Approximations


14.1 Variational Methods


14.2 Time-Independent Perturbations


14.4 Fermi's Golden Rule


14.5 Density Matrices—Random Perturbations


14.6 Response Function; Susceptibility


Part III One-Electron Atoms


Chapter 15 Dirac Equation


15.1 Free Particle Equation


15.2 Dirac Equation with Electromagnetic Coupling


Chapter 16 Hydrogen Atom


16.1 Schrödinger Equation


16.2 One-Electron Wave Functions


16.3 Spin-Orbit Coupling


16.4 Other Interactions


Chapter 17 Static Fields


17.1 Magnetic Fields


17.2 Electric Fields


Chapter 18 Hyperfine Interactions


18.1 Hamiltonian for the Magnetic Hyperfine Interaction


18.2 Magnetic Hyperfine Interaction in One-Electron Systems


18.3 Electric Quadrupole Interaction


Part IV W-Electron Atoms


Chapter 19 Hartree-Fock Formulation


19.1 The Hamiltonian


19.2 Central Field Approximation


19.3 Hartiee-Fock Equations


19.4 Properties of the Hartree-Fock Solutions


19.5 Computational Methods


19.6 Correlation Error and Configuration Interaction


Chapter 20 Multiplet Wave Functions


20.1 Two-Electron Multiplets


20.2 Terms from a Configuration of n Electrons


20.3 Construction of Multiplet Wave Functions


20.4 Symmetry Properties


20.5 jj Coupling


Chapter 21 Matrix Elements


21.1 Electrostatic Matrix Elements—Two Electrons


21.2 Some n-Electron Matrix Elements


21.3 Electrostatic Matrix Elements—n Electrons


21.4 Spin- Orbit Interaction


21.5 Conjugate Configurations


21.6 Other Interactions


Part V Electromagnetic Interactions


Chapter 22 Interaction Between Atoms and Radiation


22.1 Hamiltonian of the Radiation Field


22.2 Quantization of the Radiation Field


22.3 Interaction Hamiltonian and Matrix Elements


22.4 Selection Rules and Angular Distributions


Chapter 23 Absorption and Emission


23.1 Transition Probabilities


23.2 Einstein Coefficients and Planck's Law


23.3 Oscillator Strengths and Sum Rules


23.4 Numerical Computations


23.5 Line Broadening


23.6 Cross Sections


23.7 Photoelectric Effect


23.8 Survey of Atomic Spectra


Chapter 24 Higher Order Electromagnetic Interactions


24.1 The Kramers-Heisenberg Formula


24.2 Scattering—Special Cases


24.3 Diagrams


24.4 Optical Susceptibility and Nonlinear Effects


Part VI Molecules


Chapter 25 General Properties of Molecules


25.1 Born-Oppenheimer Approximation


25.2 Molecular Orbitals and the Self-Consistent Field Method


25.3 Computational Methods


Chapter 26 Electronic States of Molecules


26.1 Hydrogen Molecule Ion (H2+)


26.2 Symmetry Considerations—H2+


26.3 Hydrogen Molecule


26.4 Diatomic and Linear Molecules


26.5 Hybrid Orbitals


26.6 The π-Electron Approximation


Chapter 27 Molecular Spectra


27.1 Vibrations and Rotations of Diatomic Molecules


27.2 Transitions in Diatomic Molecules


27.3 Vibration of Polyatomic Molecules


27.4 Transitions in Polyatomic Molecules


Chapter 28 Ligand Fields


28.1 Basic Ideas


28.2 Single d Electron in an Octahedral and Tetragonal Field


28.3 Multielectron Configurations


28.4 Magnetic Fields and the Spin Hamiltonian


28.5 Molecular Orbitals


Appendix 1 Dirac Notation


Appendix 2 Operators


Appendix 3 Eigenvalues and Eigenfunctions


Appendix 4 Relationships Among Unit Vectors


Appendix 5 Bessel Functions


Appendix 6 Laguerre Polynomials


Appendix 7 Hermite Polynomials


Appendix 8 Dirac δ-Functions


References


Index

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