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Symmetry Principles in Solid State and Molecular Physics

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Symmetry Principles in Solid State and Molecular Physics Cover

 

Synopses & Reviews

Publisher Comments:

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, including Bravais lattices and space groups; and explains relevant applications to electron phonon scattering, optical absorption selection rules, electronic energy bands, electron dynamics, and effective Hamiltonians. Unique features of this volume include use of subgroup techniques, consideration of the influence of time reversal on selection rules, use of shell theorems and invariance techniques to construct the form of tensors, and use of broken symmetry to relate the symmetry of valence and molecular orbitals to the symmetry of electron molecular wave functions. 1974 edition. More than 200 problems. 69 black-and-white illustrations. Eight appendixes. Author Index and Bibliography. Indexes.

Book News Annotation:

This graduate textbook applies group theory to solids and molecules. The author develops invariant methods for solving vibration problems and constructing the form of crystal tensors, and describes applications to optical absorption selection rules, electronic energy bands, and effective Hamiltonians. Originally published by John Wiley in 1974.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

High-level text applies group theory to physics problems, develops methods for solving molecular vibration problems and for determining the form of crystal tensors, develops translational properties of crystals, more. 1974 edition.

Synopsis:

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.

Synopsis:

Geared toward students and professionals working on the theory of solids, this high-level volume applies group theory to solid state and molecular physics. It starts with fundamental theorems and the uses of group theory and representations, advancing to the summary of point groups, including the relation between spin and double groups. Additional features include examples in optical absorption selection rules, spin-orbit coupling and crystal field theory, plus a complete demonstration of projection techniques. Short-cut and invariant methods for solving molecular vibration problems and for determining the form of crystal tensors are discussed, along with the translational properties of crystals, including Bravais lattices and space groups. The author explains relevant applications to electron phonon scattering, optical absorption selection rules, electronic energy bands, electron dynamics, and effective Hamiltonians. Over 200 carefully selected problems.

Table of Contents

Chapter 1. Relation of Group Theory to Quantum mechanics

  1.1 Symmetry Operations

  1.2 Abstract Group Theory

  1.3 Commuting Observables and Classes

  1.4 Representations and Irreducible Representations

  1.5 Relation between Representations, Characters, and States

  1.6 Continuous Groups

  1.7 Summary

Chapter 2. Point Groups

  2.1 Generators of the Proper Rotation Group R superscript + (3)

  2.2 The Commutator Algebra of R superscript + (3)

  2.3 Irreducible Representations of R superscript + (3)

  2.4 Characters of the Irreducible Representations of R superscript + (3)

  2.5 The Three-dimensional Representation j=1 of R superscript + (3)

  2.6 The Spin Representation j=1/2 of R superscript + (3)

  2.7 Class Structure of Point Groups

  2.8 The Proper Point Groups

  2.9 Nature of Improper Rotations in a Finite Group

  2.10 Relation between Improper and Proper Groups

  2.11 Representations of Groups Containing the Inversion

  2.12 Product Groups

  2.13 Representations of an Outer Product Group

  2.14 Enumeration of the Improper Point Groups

  2.15 Crystallographic Point Groups

  2.16 Double Point Groups

  2.17 Summary

Chapter 3. Point Group Examples

  3.1 Electric and Magnetic Dipoles: Irreducible Components of a Reducible Space

  3.2 Crystal field Theory without Spin: Compatibility Relations

  3.3 Product Representations and Decomposition of Angular Momentum

  3.4 Selection rules

  3.5 Spin and Spin-Orbit Coupling

  3.6 Crystal Field Theory with Spin

  3.7 Projection Operators

  3.8 Crystal Harmonics

  3.9 Summary

Chapter 4. Macroscopic Crystal Tensors

  4.1 Macroscopic Point Group Symmetry

  4.2 Tensors of the First Rank: Ferroelectrics and Ferromagnetics

  4.3 Second-Rank Tensors: Conductivity, Susceptibility

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

  4.5 Method of Invariants

  4.6 Measures of Infinitesimal and Finite Strain

  4.7 The Elasticity Tensor for Group C subscript (3upsilon)

  4.8 Summary

Chapter 5. Molecular Vibrations

  5.1 Representations contained in NH subscript 3 vibrations

  5.2 Determination of the Symmetry Vectors for NH subscript 3

  5.3 Symmetry Coordinates, Normal Coordinates, Internal Coordinates, and Invariants

  5.4 Potential Energy and Force Constants

  5.5 The Number of Force Constants

  5.6 Summary

Chapter 6. Translational Properties of Crystals

  6.1 Crystal Systems, Bravais Lattices, and Crystal Classes

  6.2 Representations of the Translation Group

  6.3 Reciprocal Lattices and Brillouin Zones

  6.4 Character Orthonormality Theorems

  6.5 Conservation of Crystal Momentum

  6.6 Laue-Bragg X-ray Diffraction

  6.7 Summary

Chapter 7. Electronic Energy Bands

  7.1 Relation between the Many-Electron and One-Electron Viewpoints

  7.2 Concept of an Energy Band

  7.3 The Empty Lattice

  7.4 Almost-Free Electrons

  7.5 Energy Gaps and Symmetry Considerations

  7.6 Points of Zero Slope

  7.7 Periodicity in Reciprocal Space

  7.8 The k • p Method of Analytical Continuation

  7.9 Dynamics of Electron Motion in Crystals

  7.10 Effective Hamiltonians and Donor States

  7.11 Summary

Chapter 8. Space Groups

  8.1 Screw Axes and Glide Planes

  8.2 Restrictions on space Group Elements

  8.3 Equivalence of Space Groups

  8.4 Construction of Space Groups

  8.5 Factor Groups of Space Groups

  8.6 Groups G subscript k of the Wave Vector k

  8.7 Space Group Algebra

  8.8 Representations of Symmorphic Space Groups

  8.9 Representations of Nonsymmorphic Space Groups

  8.10 Class Structure and Algebraic Treatment of Multiplier Groups

  8.11 Double Space Groups

  8.12 Summary

Chapter 9. Space Group Examples

  9.1 Vanishing Electric Moment in Diamond

  9.2 Induced Quadrupole Moments in Diamond

  9.3 Force Constants in Crystals

  9.4 Local Electric Moments

  9.5 Symmetries of Acoustic and Optical Modes of Vibration

  9.6 Hole Scattering by Phonons

  9.7 Selection Rules for Direct Optical Absorption

  9.8 Summary

Chapter 10. Time reversal

  10.1 Nature of Time-Reversal Operators without Spin

  10.2 Time Reversal with Spin

  10.3 Time Reversal in External Fields

  10.4 Antilinear and Antiunitary Operators

  10.5 Onsager Relations

  10.6 The Time-Reversed Representation

  10.7 Time-reversal Degeneracies

  10.8 The Herring Criterion for Space Groups

  10.9 Selection Rules Due to Time Reversal

  10.10 Summary

Chapter 11. Lattice Vibration Spectra

  11.1 Inelastic Neutron Scattering

  11.2 Transformation to Normal Coordinates

  11.3 Quantized Lattice Oscillators: Phonons

  11.4 Crystal Momentum

  11.5 Infinitesimal Displacement and Rotational Invariance

  11.6 Symmetry Properties of the Dynamical Matrix

  11.7 Consequences of Time Reversal

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

  11.9 The Method of Long Waves: Primitive Lattices

  11.10 Nonprimitive Lattices and Internal Shifts

  11.11 Summary

Chapter 12. Vibrations of Lattices with the Diamond Structure

  12.1 Force Constants and the Dynamical Matrix

  12.2 Symmetry of Vibrations at DELTA = (q, 0, 0)

  12.3 R(q) and omega(q) for q = (q, 0, 0)

  12.4 Sigma Sum Modes (q, q, 0)

  12.5 The Modes LAMBDA = (q, q, q) and L = (2 pi/a)(1/2, 1/2, 1/2)

  12.6 Elastic Properties of the Diamond Structure

  12.7 Comparison with Experiment

  12.8 Summary

Chapter 13. Symmetry of Molecular Wave Functions

  13.1 Molecular Orbital Theory

  13.2 Valence Bond Orbitals

  13.3 Many-Body Wave functions and Chemical Structures

  13.4 Hartree-Fock Wave Functions and Broken Symmetry

  13.5 The Jahn-Teller Effect

  13.6 Summary

Appendix A. Character Tables and Basis Functions for the Single and Double Point Groups

Appendix B. Schoenflies, International, and Herring Notations

Appendix C. Decomposition of D subscript J superscript plus/minus of Full Rotation Group into Point Group Representations

Appendix D. Orthogonality Properties of Eigenvectors of the Equation alpha PSI = lambda B PSI; Reciprocals of Singular Matrices

Appendix E. The Brillouin Zones

Appendix F. Multiplier Representations for the Point Groups

Appendix G. Wigner Mappings and the Fundamental Theorem of Projective Geometry

Appendix H. Generalized Mobility Theory

  Author Index and Bibliography; Subject Index; Symbol Index

Product Details

ISBN:
9780486420011
Author:
Lax, Melvin J.
Publisher:
Dover Publications
Author:
Lax, Melvin
Location:
Mineola, N.Y.
Subject:
Physics
Subject:
Solid State Physics
Subject:
Group Theory
Subject:
Molecules
Subject:
Lattice theory
Subject:
Symmetry
Subject:
Symmetry (Physics)
Subject:
Physics-Solid State Physics
Edition Description:
Trade Paper
Series:
Dover Books on Physics
Series Volume:
F102
Publication Date:
20120331
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
512
Dimensions:
8.25 x 5.38 in 1.46 lb

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Science and Mathematics » Physics » Solid State Physics

Symmetry Principles in Solid State and Molecular Physics New Trade Paper
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Product details 512 pages Dover Publications - English 9780486420011 Reviews:
"Synopsis" by ,
High-level text applies group theory to physics problems, develops methods for solving molecular vibration problems and for determining the form of crystal tensors, develops translational properties of crystals, more. 1974 edition.
"Synopsis" by ,
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.
"Synopsis" by , Geared toward students and professionals working on the theory of solids, this high-level volume applies group theory to solid state and molecular physics. It starts with fundamental theorems and the uses of group theory and representations, advancing to the summary of point groups, including the relation between spin and double groups. Additional features include examples in optical absorption selection rules, spin-orbit coupling and crystal field theory, plus a complete demonstration of projection techniques. Short-cut and invariant methods for solving molecular vibration problems and for determining the form of crystal tensors are discussed, along with the translational properties of crystals, including Bravais lattices and space groups. The author explains relevant applications to electron phonon scattering, optical absorption selection rules, electronic energy bands, electron dynamics, and effective Hamiltonians. Over 200 carefully selected problems.
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