Atoms and Molecules

Atoms and Molecules

1st Edition - January 1, 1978

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  • Author: Mitchel Weissbluth
  • eBook ISBN: 9780323142946

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Description

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.

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

Product details

  • No. of pages: 730
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: January 1, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9780323142946

About the Author

Mitchel Weissbluth

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