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Symmetry Principles in Solid State and Molecular Physics,9780486420011

Symmetry Principles in Solid State and Molecular Physics

by
Format: Paperback
Pub. Date: 3/14/2012
Publisher(s): Dover Publications
Availability: This title is currently not available.

Summary

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.

Table of Contents

Relation of Group Theory to Quantum Mechanics
1(33)
Symmetry Operations
2(4)
Abstract Group Theory
6(3)
Commuting Observables and Classes
9(4)
Representations and Irreducible Representations
13(6)
Relation between Representations, Characters, and States
19(6)
Continuous Groups
25(4)
Summary
29(5)
Point Groups
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 Three-Dimensional 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)
The Proper Point Groups
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)
Product Groups
56(1)
Representations of and Outer Product Group
57(1)
Enumeration of the Improper Point Groups
58(3)
Crystallographic Point Groups
61(1)
Double Point Groups
62(2)
Summary
64(5)
Point Group Examples
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)
Selection Rules
82(7)
Spin and Spin-Orbit Coupling
89(4)
Crystal Field Theory with Spin
93(6)
Projection Operators
99(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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