Symmetry Principles in Solid State and Molecular Physics

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ISBN: 9780486420011 | 0486420019
Cover: Paperback
Copyright: 3/14/2012

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High-level text applies group theory to solid state and molecular physics. The author develops short-cut and invariant methods for solving molecular vibration problems and for determining the form of crystal tensors; develops the translational properties of crystals; and explains relevant applications. 69 illustrations. 1974 edition.

Relation of Group Theory to Quantum Mechanics

(33)

Symmetry Operations

(4)

Abstract Group Theory

(3)

Commuting Observables and Classes

(4)

Representations and Irreducible Representations

(6)

Relation between Representations, Characters, and States

(6)

Continuous Groups

(4)

Summary

(5)

Point Groups

(35)

Generators of the Proper Rotation Group R+(3)

(2)

The Commutator Algebra of R+(3)

(1)

Irreducible Representations of R+(3)

(1)

Characters of the Irreducible Representations of R+(3)

(1)

The Three-Dimensional Representation j=1 of R+(3)

(3)

The Spin Representation j=½ of R+(3)

(4)

Class Structure of Point Groups

(2)

The Proper Point Groups

(2)

Nature of Improper Rotations in a Finite Group

(3)

Relation between Improper and Proper Groups

(1)

Representations of Groups Containing the Inversion

(1)

Product Groups

(1)

Representations of and Outer Product Group

(1)

Enumeration of the Improper Point Groups

(3)

Crystallographic Point Groups

(1)

Double Point Groups

(2)

Summary

(5)

Point Group Examples

(42)

Electric and Magnetic Dipoles: Irreducible Components of a Reducible Space

(4)

Crystal Field Theory without Spin: Compatibility Relations

(4)

Product Representations and Decomposition of Angular Momentum

(5)

Selection Rules

(7)

Spin and Spin-Orbit Coupling

(4)

Crystal Field Theory with Spin

(6)

Projection Operators

(2)

Crystal Harmonics

101

(4)

Summary

105

(6)

Macroscopic Crystal Tensors

111

(23)

Macroscopic Point Group Symmetry

111

(1)

Tensors of the First Rank: Ferroelectrics and Ferromagnetics

112

(2)

Second-Rank Tensors: Conductivity, Susceptibility

114

(4)

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

118

(2)

Method of Invariants

120

(4)

Measures of Infinitesimal and Finite Strain

124

(5)

The Elasticity Tensor for Group C3v

129

(1)

Summary

130

(4)

Molecular Vibrations

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)

Summary

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)

Laue-Bragg X-ray Diffraction

189

(3)

Summary

192

(2)

Electronic Energy Bands

194

(37)

Relation between the Many-Electron and One-Electron Viewpoints

195

(3)

Concept of an Energy Band

198

(1)

The Empty Lattice

199

(2)

Almost-Free Electrons

201

(3)

Energy Gaps and Symmetry Considerations

204

(2)

Points of Zero Slope

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)

Summary

227

(4)

Space Groups

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)

Space Group Algebra

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)

Double Space Groups

250

(2)

Summary

252

(4)

Space Group Examples

256

(19)

Vanishing Electric Moment in Diamond

256

(4)

Induced Quadrupole Moments in Diamond

260

(1)

Force Constants in Crystals

261

(3)

Local Electric Moments

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)

Summary

273

(2)

Time Reversal

275

(49)

Nature of Time-Reversal Operators without Spin

275

(2)

Time Reversal with Spin

277

(3)

Time Reversal in External Fields

280

(1)

Antilinear and Antiunitary Operators

281

(6)

Onsager Relations

287

(5)

The Time-Reversed Representation

292

(9)

Time-Reversal Degeneracies

301

(4)

The Herring Criterion for Space Groups

305

(7)

Selection Rules Due to Time Reversal

312

(7)

Summary

319

(5)

Lattice Vibration Spectra

324

(39)

Inelastic Neutron Scattering

324

(2)

Transformation to Normal Coordinates

326

(5)

Quantized Lattice Oscillators: Phonons

331

(2)

Crystal Momentum

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)

Summary

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)

Σ Modes (q,q,0)

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)

Summary

388

(2)

Symmetry of Molecular Wave Functions

390

(26)

Molecular Orbital Theory

390

(3)

Valence Bond Orbitals

393

(11)

Many-Body Wave Functions and Chemical Structures

404

(5)

Hartree-Fock Wave Functions and Broken Symmetry

409

(4)

The Jahn-Teller Effect

413

(1)

Summary

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

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Symmetry Principles in Solid State and Molecular Physics

Summary

Table of Contents

Supplemental Materials