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Symmetry Principles in Solid State and Molecular Physics

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ISBN-10: 0486420019

ISBN-13: 9780486420011

Edition: 2001

Authors: Melvin J. Lax

List price: $25.95
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Book details

List price: $25.95
Copyright year: 2001
Publisher: Dover Publications, Incorporated
Publication date: 3/14/2012
Binding: Hardcover
Pages: 512
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.386
Language: English

Relation of Group Theory to Quantum mechanics
Symmetry Operations
Abstract Group Theory
Commuting Observables and Classes
Representations and Irreducible Representations
Relation between Representations, Characters, and States
Continuous Groups
Summary
Point Groups
Generators of the Proper Rotation Group R superscript + (3)
The Commutator Algebra of R superscript + (3)
Irreducible Representations of R superscript + (3)
Characters of the Irreducible Representations of R superscript + (3)
The Three-dimensional Representation j=1 of R superscript + (3)
The Spin Representation j=1/2 of R superscript + (3)
Class Structure of Point Groups
The Proper Point Groups
Nature of Improper Rotations in a Finite Group
Relation between Improper and Proper Groups
Representations of Groups Containing the Inversion
Product Groups
Representations of an Outer Product Group
Enumeration of the Improper Point Groups
Crystallographic Point Groups
Double Point Groups
Summary
Point Group Examples
Electric and Magnetic Dipoles: Irreducible Components of a Reducible Space
Crystal field Theory without Spin: Compatibility Relations
Product Representations and Decomposition of Angular Momentum
Selection rules
Spin and Spin-Orbit Coupling
Crystal Field Theory with Spin
Projection Operators
Crystal Harmonics
Summary
Macroscopic Crystal Tensors
Macroscopic Point Group Symmetry
Tensors of the First Rank: Ferroelectrics and Ferromagnetics
Second-Rank Tensors: Conductivity, Susceptibility
Direct Inspection Methods for Tensors of Higher Rank: the Hall Effect
Method of Invariants
Measures of Infinitesimal and Finite Strain
The Elasticity Tensor for Group C subscript (3upsilon)
Summary
Molecular Vibrations
Representations contained in NH subscript 3 vibrations
Determination of the Symmetry Vectors for NH subscript 3
Symmetry Coordinates, Normal Coordinates, Internal Coordinates, and Invariants
Potential Energy and Force Constants
The Number of Force Constants
Summary
Translational Properties of Crystals
Crystal Systems, Bravais Lattices, and Crystal Classes
Representations of the Translation Group
Reciprocal Lattices and Brillouin Zones
Character Orthonormality Theorems
Conservation of Crystal Momentum
Laue-Bragg X-ray Diffraction
Summary
Electronic Energy Bands
Relation between the Many-Electron and One-Electron Viewpoints
Concept of an Energy Band
The Empty Lattice
Almost-Free Electrons
Energy Gaps and Symmetry Considerations
Points of Zero Slope
Periodicity in Reciprocal Space
The k • p Method of Analytical Continuation
Dynamics of Electron Motion in Crystals
Effective Hamiltonians and Donor States
Summary
Space Groups
Screw Axes and Glide Planes
Restrictions on space Group Elements
Equivalence of Space Groups
Construction of Space Groups
Factor Groups of Space Groups
Groups G subscript k of the Wave Vector k
Space Group Algebra
Representations of Symmorphic Space Groups
Representations of Nonsy