
Relation of Group Theory to Quantum Mechanics 


1  (33) 


2  (4) 


6  (3) 

Commuting Observables and Classes 


9  (4) 

Representations and Irreducible Representations 


13  (6) 

Relation between Representations, Characters, and States 


19  (6) 


25  (4) 


29  (5) 


34  (35) 

Generators of the Proper Rotation Group R+(3) 


35  (2) 

The Commutator Algebra of R+(3) 


37  (1) 

Irreducible Representations of R+(3) 


38  (1) 

Characters of the Irreducible Representations of R+(3) 


39  (1) 

The ThreeDimensional Representation j=1 of R+(3) 


40  (3) 

The Spin Representation j=½ of R+(3) 


43  (4) 

Class Structure of Point Groups 


47  (2) 


49  (2) 

Nature of Improper Rotations in a Finite Group 


51  (3) 

Relation between Improper and Proper Groups 


54  (1) 

Representations of Groups Containing the Inversion 


55  (1) 


56  (1) 

Representations of and Outer Product Group 


57  (1) 

Enumeration of the Improper Point Groups 


58  (3) 

Crystallographic Point Groups 


61  (1) 


62  (2) 


64  (5) 


69  (42) 

Electric and Magnetic Dipoles: Irreducible Components of a Reducible Space 


69  (4) 

Crystal Field Theory without Spin: Compatibility Relations 


73  (4) 

Product Representations and Decomposition of Angular Momentum 


77  (5) 


82  (7) 

Spin and SpinOrbit Coupling 


89  (4) 

Crystal Field Theory with Spin 


93  (6) 


99  (2) 


101  (4) 


105  (6) 

Macroscopic Crystal Tensors 


111  (23) 

Macroscopic Point Group Symmetry 


111  (1) 

Tensors of the First Rank: Ferroelectrics and Ferromagnetics 


112  (2) 

SecondRank Tensors: Conductivity, Susceptibility 


114  (4) 

Direct Inspection Methods for Tensors of Higher Rank: the Hall Effect 


118  (2) 


120  (4) 

Measures of Infinitesimal and Finite Strain 


124  (5) 

The Elasticity Tensor for Group C3v 


129  (1) 


130  (4) 


134  (35) 

Representations Contained in NH3 Vibrations 


135  (4) 

Determination of the Symmetry Vectors for NH3 


139  (7) 

Symmetry Coordinates, Normal Coordinates, Internal Coordinates, and Invariants 


146  (7) 

Potential Energy and Force Constants 


153  (8) 

The Number of Force Constants 


161  (4) 


165  (4) 

Translational Properties of Crystals 


169  (25) 

Crystal Systems, Bravais Lattices, and Crystal Classes 


169  (12) 

Representations of the Translation Group 


181  (4) 

Reciprocal Lattices and Brillouin Zones 


185  (1) 

Character Orthonormality Theorems 


186  (2) 

Conservation of Crystal Momentum 


188  (1) 

LaueBragg Xray Diffraction 


189  (3) 


192  (2) 


194  (37) 

Relation between the ManyElectron and OneElectron Viewpoints 


195  (3) 

Concept of an Energy Band 


198  (1) 


199  (2) 


201  (3) 

Energy Gaps and Symmetry Considerations 


204  (2) 


206  (2) 

Periodicity in Reciprocal Space 


208  (3) 

The kp Method of Analytical Continuation 


211  (9) 

Dynamics of Electron Motion in Crystals 


220  (4) 

Effective Hamiltonians and Donor States 


224  (3) 


227  (4) 


231  (25) 

Screw Axes and Glide Planes 


231  (1) 

Restrictions on Space Group Elements 


232  (3) 

Equivalence of Space Groups 


235  (1) 

Construction of Space Groups 


236  (2) 

Factor Groups of Space Groups 


238  (2) 

Group Gk of the Wave Vector k 


240  (3) 


243  (1) 

Representations of Symmorphic Space Groups 


244  (1) 

Representations of Nonsymmorphic Space Groups 


244  (3) 

Class Structure and Algebraic Treatment of Multiplier Groups 


247  (3) 


250  (2) 


252  (4) 


256  (19) 

Vanishing Electric Moment in Diamond 


256  (4) 

Induced Quadrupole Moments in Diamond 


260  (1) 

Force Constants in Crystals 


261  (3) 


264  (3) 

Symmetries of Acoustic and Optical Modes of Vibration 


267  (3) 

Hole Scattering by Phonons 


270  (1) 

Selection Rules for Direct Optical Absorption 


271  (2) 


273  (2) 


275  (49) 

Nature of TimeReversal Operators without Spin 


275  (2) 


277  (3) 

Time Reversal in External Fields 


280  (1) 

Antilinear and Antiunitary Operators 


281  (6) 


287  (5) 

The TimeReversed Representation 


292  (9) 

TimeReversal Degeneracies 


301  (4) 

The Herring Criterion for Space Groups 


305  (7) 

Selection Rules Due to Time Reversal 


312  (7) 


319  (5) 

Lattice Vibration Spectra 


324  (39) 

Inelastic Neutron Scattering 


324  (2) 

Transformation to Normal Coordinates 


326  (5) 

Quantized Lattice Oscillators: Phonons 


331  (2) 


333  (2) 

Infinitesimal Displacement and Rotational Invariance 


335  (1) 

Symmetry Properties of the Dynamical Matrix 


336  (4) 

Consequences of Time Reversal 


340  (4) 

Form and Number of Independent Constants in the Dynamical Matrix for Internal and Zone Boundary Points 


344  (2) 

The Method of Long Waves: Primitive Lattices 


346  (4) 

Nonprimitive Lattices and Internal Shifts 


350  (7) 


357  (6) 

Vibrations of Lattices with the Diamond Structure 


363  (27) 

Force Constants and the Dynamical Matrix 


363  (3) 

Symmetry of Vibrations at δ=(q,0,0) 


366  (8) 

R(q) and Sigma;(q) for q=(q,0,0) 


374  (3) 


377  (5) 

The Modes A=(q,q,q) and L=(2π/a)(&haif;,½,½) 


382  (3) 

Elastic Properties of the Diamond Structure 


385  (2) 

Comparison with Experiment 


387  (1) 


388  (2) 

Symmetry of Molecular Wave Functions 


390  (26) 


390  (3) 


393  (11) 

ManyBody Wave Functions and Chemical Structures 


404  (5) 

HartreeFock Wave Functions and Broken Symmetry 


409  (4) 


413  (1) 


414  (2) 
Appendix A. Character Tables and Basis Functions for the Single and Double Point Groups 

416  (17) 
Appendix B. Schoenflies, International, and Herring Notations 

433  (3) 
Appendix C. Decomposition of Dj± of Full Rotation Group into Point Group Representations 

436  (3) 
Appendix D. Orthogonality Properties of Eigenvectors of the Equation AΠ=ΛBΠ; Reciprocals of Singular Matrices 

439  (4) 
Appendix E. The Brillouin Zones 

443  (9) 
Appendix F. Multiplier Representations for the Point Groups 

452  (9) 
Appendix G. Wigner Mappings and the Fundamental Theorem of Projective Geometry 

461  (5) 
Appendix H. Generalized Mobility Theory 

466  (3) 
Author Index and Bibliography 

469  (12) 
Subject Index 

481  (10) 
Symbol Index 

491  