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Group theory: application to the physics of condensed matter

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Hauptverfasser:	Dresselhaus, Mildred S. 1930-2017 (VerfasserIn), Dresselhaus, Gene 1929- (VerfasserIn), Jorio, Ado (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin Springer 2008
Schlagworte:	Gruppentheorie Festkörperphysik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Beschreibung:	XV, 582 Seiten Illustrationen
ISBN:	9783540328971 9783642069451

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Datensatz im Suchindex

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adam_text	Contents Part I Basic Mathematics 1 Basic Mathematical Background: Introduction ............. 3 1.1 Definition of a Group .................................... 3 1.2 Simple Example of a Group .............................. 3 1.3 Basic Definitions ........................................ 6 1.4 Rearrangement Theorem ................................. 7 1.5 Cosets ................................................. 7 1.6 Conjugation and Class ................................... 9 1.7 Factor Groups .......................................... 11 1.8 Group Theory and Quantum Mechanics ................... 11 2 Representation Theory and Basic Theorems ............... 15 2.1 Important Definitions ................................... 15 2.2 Matrices ............................................... 16 2.3 Irreducible Representations .............................. 17 2.4 The Unitarity of Representations ......................... 19 2.5 Schurs Lemma (Part 1) ................................. 21 2.6 Schur s Lemma (Part 2) ................................. 23 2.7 Wonderful Orthogonality Theorem ........................ 25 2.8 Representations and Vector Spaces ........................ 28 3 Character of a Representation ............................. 29 3.1 Definition of Character .................................. 29 3.2 Characters and Class .................................... 30 3.3 Wonderful Orthogonality Theorem for Character ............ 31 3.4 Reducible Representations ............................... 33 3.5 The Number of Irreducible Representations ................ 35 3.6 Second Orthogonality Relation for Characters .............. 36 3.7 Regular Representation .................................. 37 3.8 Setting up Character Tables .............................. 40 X Contents 3.9 Schoenflies Symmetry Notation ........................... 44 3.10 The Herniann-Mauguin Symmetry Notation ............... 46 3.11 Symmetry Relations and Point Group Classifications ........ 48 4 Basis Functions ............................................ 57 4.1 Symmetry Operations and Basis Functions ................. 57 4.2 Basis Functions for Irreducible Representations ............. 58 4.3 Projection Operators P^f 1 .............................. 64 4.4 Derivation of an Explicit Expression for Pj.e .............. 64 4.5 The Effect of Projection Operations on an Arbitrary Function 65 4.6 Linear Combinations of Atomic Orbitals for Three Equivalent Atoms at the Corners of an Equilateral Triangle . . 67 4.7 The Application of Group Theory to Quantum Mechanics .... 70 Part II Introductory Application to Quantum Systems 5 Splitting of Atomic Orbitals in a Crystal Potential ......... 79 5.1 Introduction ........................................... 79 5.2 Characters for the Full Rotation Group .................... 81 5.3 Cubic Crystal Field Environment for a Paramagnetic Transition Metal Ion ................... 85 5.4 Comments on Basis Functions ............................ 90 5.5 Comments on the Form of Crystal Fields .................. 92 6 Application to Selection Rules and Direct Products ....... 97 6.1 The Electromagnetic Interaction as a Perturbation .......... 97 6.2 Orthogonality of Basis Functions .......................... 99 6.3 Direct Product of Two Groups ...........................100 6.4 Direct Product of Two Irreducible Representations ..........101 6.5 Characters for the Direct Product .........................103 6.6 Selection Rule Concept in Group Theoretical Terms .........105 6.7 Example of Selection Rules ...............................106 Part III Molecular Systems 7 Electronic States of Molecules and Directed Valence .......113 7.1 Introduction ...........................................113 7.2 General Concept of Equivalence ..........................115 7.3 Directed Valence Bonding ................................117 7.4 Diatomic Molecules .....................................118 7.4.1 Homonuclear Diatomic Molecules ...................118 7.4.2 Heterogeneous Diatomic Molecules ..................120 Contents XI 7.5 Electronic Orbitals for Mułtiatomic Molecules ..............124 7.5.1 The NH3 Molecule ................................124 7.5.2 The CH4 Molecule ................................125 7.5.3 The Hypothetical SH6 Molecule ....................129 7.5.4 The Octahedral SF6 Molecule ......................133 7.6 σ- and тг -Bonds ......................................... 134 7.7 Jahn-Teller Effect ......................................141 Molecular Vibrations, Infrared, and Raman Activity .......147 8.1 Molecular Vibrations: Background ........................147 8.2 Application of Group Theory to Molecular Vibrations .......149 8.3 Finding the Vibrational Normal Modes ....................152 8.4 Molecular Vibrations in H2O .............................154 8.5 Overtones and Combination Modes .......................156 8.6 Infrared Activity ........................................157 8.7 Raman Effect ..........................................159 8.8 Vibrations for Specific Molecules ..........................161 8.8.1 The Linear Molecules .............................161 8.8.2 Vibrations of the NH3 Molecule ....................166 8.8.3 Vibrations of the CH4 Molecule ....................168 8.9 Rotational Energy Levels ................................170 8.9.1 The Rigid Rotator ................................170 8.9.2 Wigner -Eckart Theorem ...........................172 8.9.3 Vibrational-Rotational Interaction ..................174 Part IV Application to Periodic Lattices 9 Space Groups in Real Space ...............................183 9.1 Mathematical Background for Space Groups ...............184 9.1.1 Space Groups Symmetry Operations ................184 9.1.2 Compound Space Group Operations ................186 9.1.3 Translation Subgroup .............................188 9.1.4 Symmorphic and Nonsymmorphic Space Groups ......189 9.2 Bravais Lattices and Space Groups ........................190 9.2.1 Examples of Symmorphic Space Groups .............192 9.2.2 Cubic Space Groups and the Equivalence Transformation ................194 9.2.3 Examples of Nonsynimorphic Space Groups ..........196 9.3 Two-Dimensional Space Group.s ..........................198 9.3.1 2D Oblique Space Groups ..........................200 9.3.2 2D Rectangular Space Groups ......................201 9.3.3 2D Square Space Group ...........................203 9.3.4 2D Hexagonal Space Groups .......................203 9.4 Line Groups ............................................204 XII Contents 9.5 The Determination of Crystal Structure and Space Group .... 205 9.5.1 Determination of the Crystal Structure ..............206 9.5.2 Determination of the Space Group ..................206 10 Space Groups in Reciprocal Space and Representations .... 209 10.1 Reciprocal Space ........................................210 10.2 Translation Subgroup ...................................211 10.2.1 Representations for the Translation Group ...........211 10.2.2 Bloch s Theorem and the Basis of the Translational Group .........................212 10.3 Symmetry of к Vectors and the Group of the Wave Vector . . . 214 10.3.1 Point Group Operation in r-space and fe-space .......214 10.3.2 The Group of the Wave Vector Gk and the Star of к . . 215 10.3.3 Effect of Translations and Point Group Operations on Bloch Functions ...............................215 10.4 Space Group Representations .............................219 10.4.1 Symmorphic Group Representations .................219 10.4.2 Nonsymmorphic Group Representations and the Multiplier Algebra .........................220 10.5 Characters for the Equivalence Representation ..............221 10.6 Common Cubic Lattices: Symmorphic Space Groups ........222 10.6.1 The Г Point .....................................223 10.6.2 Points with к φ 0.................................224 10.7 Compatibility Relations .................................227 10.8 The Diamond Structure: Nonsymmorphic Space Group ......230 10.8.1 Factor Group and the Γ Point ......................231 10.8.2 Points with к Φ 0.................................232 10.9 Finding Character Tables for all Groups of the Wave Vector . . 235 Part V Electron and Phonon Dispersion Relation 11 Applications to Lattice Vibrations .........................241 11.1 Introduction ...........................................241 11.2 Lattice Modes and Molecular Vibrations ...................244 11.3 Zone Center Phonon Modes ..............................246 11.3.1 The NaCl Structure ...............................246 11.3.2 The Perovskite Structure ..........................247 11.3.3 Phonons in the Nonsymmorphic Diamond Lattice .....250 11.3.4 Phonons in the Zinc Blende Structure ...............252 11.4 Lattice Modes Away from fc = 0..........................253 11.4.1 Phonons in NaCl at the X Point A- = (тг/о)(100) ......254 11.4.2 Phonons in BaTiO3 at the X Point .................256 11.4.3 Phonons at the К Point in Two-Dimensional Graphite. 258 Contents XIII 11.5 Phonons in Te and α -Quartz Nonsymmorphic Structures .....262 11.5.1 Phonons in Tellurium............................. 262 11.5.2 Phonons in the α -Quartz Structure .................268 11.6 Effect of Axial Stress on Phonons .........................272 12 Electronic Energy Levels in a Cubic Crystals ..............279 12.1 Introduction ...........................................279 12.2 Plane Wave Solutions at к = 0 ...........................282 12.3 Symmetrized Plane Solution Waves along the Zi- Axis ........286 12.4 Plane Wave Solutions at the X Point ......................288 12.5 Effect of Glide Planes and Screw Axes .....................294 13 Energy Band Models Based on Symmetry .................305 13.1 Introduction ...........................................305 13.2 к ■ ρ Perturbation Theory ................................307 13.3 Example of к ■ ρ Perturbation Theory for a Nondegenerate Г^ Band ............................308 13.4 Two Band Model: Degenerate First-Order Perturbation Theory ...............311 13.5 Degenerate second-order к ■ ρ Perturbation Theory ..........316 13.6 Nondegenerate к ■ ρ Perturbation Theory at a Δ Point ......324 13.7 Use of к ■ ρ Perturbation Theory to Interpret Optical Experiments .........................326 13.8 Application of Group Theory to Valley-Orbit Interactions in Semiconductors ......................................327 13.8.1 Background ......................................328 13.8.2 Impurities in Multivalley Semiconductors ............330 13.8.3 The Valley-Orbit Interaction .......................331 14 Spin-Orbit Interaction in Solids and Double Groups .......337 14.1 Introduction ...........................................337 14.2 Crystal Double Groups ..................................341 14.3 Double Group Properties ................................343 14.4 Crystal Field Splitting Including Spin-Orbit Coupling .......349 14.5 Basis Functions for Double Group Representations ..........353 14.6 Some Explicit Basis Functions ............................355 14.7 Basis Functions for Other Г8+ States ......................358 14.8 Comments on Double Group Character Tables ..............359 14.9 Plane Wave Basis Functions for Double Group Representations ........................360 14.10 Group of the Wave Vector for Nonsymmorphic Double Groups .......................362 XIV Contents 15 Application of Double Groups to Energy Bands with Spin . 367 15.1 Introduction ...........................................367 15.2 E(k) for the Empty Lattice Including Spin-Orbit Interaction . 368 15.3 The к ■ ρ Perturbation with Spin-Orbit Interaction .........369 15.4 E (к) for a Nondegenerate Band Including Spin-Orbit Interaction ..................................372 15.5 E (к) for Degenerate Bands Including Spin-Orbit Interaction . 374 15.6 Effective ¿/-Factor .......................................378 15.7 Fourier Expansion of Energy Bands: Slater-Koster Method .. . 389 15.7.1 Contributions at d = 0 ............................396 15.7.2 Contributions at d = 1 ............................396 15.7.3 Contributions at d = 2 ............................397 15.7.4 Summing Contributions through d = 2 ..............397 15.7.5 Other Degenerate Levels ...........................397 Part VI Other Symmetries 16 Time Reversal Symmetry ..................................403 16.1 The Time Reversal Operator .............................403 16.2 Properties of the Time Reversal Operator ..................404 16.3 The Effect of Τ on E{k), Neglecting Spin ..................407 16.4 The Effect of Ť on E{k), Including the Spin-Orbit Interaction ...............................411 16.5 Magnetic Groups .......................................416 16.5.1 Introduction .....................................418 16.5.2 Types of Elements ................................418 16.5.3 Types of Magnetic Point Groups ....................419 16.5.4 Properties of the 58 Magnetic Point Groups {A¡.Mk} .419 16.5.5 Exanrples of Magnetic Structures ...................423 16.5.6 Effect of Symmetry on the Spin Hamiltonian for the 32 Ordinary Point. Groups ...................426 17 Permutation Groups and Many-Electron States ............431 17.1 Introduction ...........................................432 17.2 Classes and Irreducible Representations of Permutation Groups ..................................434 17.3 Basis Functions of Permutation Groups ....................437 17.4 Pauli Principle in Atomic Spectra .........................440 17.4.1 Two-Electron States ..............................440 17.4.2 Three-Electron States .............................443 17.4.3 Four-Electron States ..............................448 17.4.4 Five-Electron States ...............................451 17.4.5 General Comments on Manv-Electron States .........451 Contents XV 18 Symmetry Properties of Tensors ...........................455 18.1 Introduction ...........................................455 18.2 Independent Components of Tensors Under Permutation Group Symmetry ......................458 18.3 Independent Components of Tensors: Point Symmetry Groups .................................462 18.4 Independent Components of Tensors Under Full Rotational Symmetry .........................463 18.5 Tensors in Nonlinear Optics ..............................463 18.5.1 Cubic Symmetry: 0h ..............................464 18.5.2 Tetrahedral Symmetry: T</ .........................466 18.5.3 Hexagonal Symmetry: D^h .........................466 18.6 Elastic Modulus Tensor ..................................467 18.6.1 Full Rotational Symmetry: 3D Lsotropy ..............469 18.6.2 Icosahedral Symmetry .............................472 18.6.3 Cubic Symmetry ..................................472 18.6.4 Other Symmetry Groups ..........................474 A Point Group Character Tables .............................479 В Two-Dimensional Space Groups ...........................489 С Tables for 3D Space Groups ...............................499 C.I Real Space .............................................499 C.2 Reciprocal Space ........................................503 D Tables for Double Groups .................................521 E Group Theory Aspects of Carbon Nanotubes ..............533 E.I Nanotube Geometry and the (». m) Indices ................534 E.2 Lattice Vectors in Real Space .............................534 E.3 Lattice Vectors in Reciprocal Space .......................535 E.4 Compound Operations and Tube Helicity ..................536 E. 5 Character Tables for Carbon Nanotubes ...................538 F Permutation Group Character Tables ......................543 References .....................................................549 Index ..........................................................553
adam_txt	Contents Part I Basic Mathematics 1 Basic Mathematical Background: Introduction . 3 1.1 Definition of a Group . 3 1.2 Simple Example of a Group . 3 1.3 Basic Definitions . 6 1.4 Rearrangement Theorem . 7 1.5 Cosets . 7 1.6 Conjugation and Class . 9 1.7 Factor Groups . 11 1.8 Group Theory and Quantum Mechanics . 11 2 Representation Theory and Basic Theorems . 15 2.1 Important Definitions . 15 2.2 Matrices . 16 2.3 Irreducible Representations . 17 2.4 The Unitarity of Representations . 19 2.5 Schurs Lemma (Part 1) . 21 2.6 Schur "s Lemma (Part 2) . 23 2.7 Wonderful Orthogonality Theorem . 25 2.8 Representations and Vector Spaces . 28 3 Character of a Representation . 29 3.1 Definition of Character . 29 3.2 Characters and Class . 30 3.3 Wonderful Orthogonality Theorem for Character . 31 3.4 Reducible Representations . 33 3.5 The Number of Irreducible Representations . 35 3.6 Second Orthogonality Relation for Characters . 36 3.7 Regular Representation . 37 3.8 Setting up Character Tables . 40 X Contents 3.9 Schoenflies Symmetry Notation . 44 3.10 The Herniann-Mauguin Symmetry Notation . 46 3.11 Symmetry Relations and Point Group Classifications . 48 4 Basis Functions . 57 4.1 Symmetry Operations and Basis Functions . 57 4.2 Basis Functions for Irreducible Representations . 58 4.3 Projection Operators P^f"1 . 64 4.4 Derivation of an Explicit Expression for Pj.e "'. 64 4.5 The Effect of Projection Operations on an Arbitrary Function 65 4.6 Linear Combinations of Atomic Orbitals for Three Equivalent Atoms at the Corners of an Equilateral Triangle . . 67 4.7 The Application of Group Theory to Quantum Mechanics . 70 Part II Introductory Application to Quantum Systems 5 Splitting of Atomic Orbitals in a Crystal Potential . 79 5.1 Introduction . 79 5.2 Characters for the Full Rotation Group . 81 5.3 Cubic Crystal Field Environment for a Paramagnetic Transition Metal Ion . 85 5.4 Comments on Basis Functions . 90 5.5 Comments on the Form of Crystal Fields . 92 6 Application to Selection Rules and Direct Products . 97 6.1 The Electromagnetic Interaction as a Perturbation . 97 6.2 Orthogonality of Basis Functions . 99 6.3 Direct Product of Two Groups .100 6.4 Direct Product of Two Irreducible Representations .101 6.5 Characters for the Direct Product .103 6.6 Selection Rule Concept in Group Theoretical Terms .105 6.7 Example of Selection Rules .106 Part III Molecular Systems 7 Electronic States of Molecules and Directed Valence .113 7.1 Introduction .113 7.2 General Concept of Equivalence .115 7.3 Directed Valence Bonding .117 7.4 Diatomic Molecules .118 7.4.1 Homonuclear Diatomic Molecules .118 7.4.2 Heterogeneous Diatomic Molecules .120 Contents XI 7.5 Electronic Orbitals for Mułtiatomic Molecules .124 7.5.1 The NH3 Molecule .124 7.5.2 The CH4 Molecule .125 7.5.3 The Hypothetical SH6 Molecule .129 7.5.4 The Octahedral SF6 Molecule .133 7.6 σ- and тг -Bonds . 134 7.7 Jahn-Teller Effect .141 Molecular Vibrations, Infrared, and Raman Activity .147 8.1 Molecular Vibrations: Background .147 8.2 Application of Group Theory to Molecular Vibrations .149 8.3 Finding the Vibrational Normal Modes .152 8.4 Molecular Vibrations in H2O .154 8.5 Overtones and Combination Modes .156 8.6 Infrared Activity .157 8.7 Raman Effect .159 8.8 Vibrations for Specific Molecules .161 8.8.1 The Linear Molecules .161 8.8.2 Vibrations of the NH3 Molecule .166 8.8.3 Vibrations of the CH4 Molecule .168 8.9 Rotational Energy Levels .170 8.9.1 The Rigid Rotator .170 8.9.2 Wigner -Eckart Theorem .172 8.9.3 Vibrational-Rotational Interaction .174 Part IV Application to Periodic Lattices 9 Space Groups in Real Space .183 9.1 Mathematical Background for Space Groups .184 9.1.1 Space Groups Symmetry Operations .184 9.1.2 Compound Space Group Operations .186 9.1.3 Translation Subgroup .188 9.1.4 Symmorphic and Nonsymmorphic Space Groups .189 9.2 Bravais Lattices and Space Groups .190 9.2.1 Examples of Symmorphic Space Groups .192 9.2.2 Cubic Space Groups and the Equivalence Transformation .194 9.2.3 Examples of Nonsynimorphic Space Groups .196 9.3 Two-Dimensional Space Group.s .198 9.3.1 2D Oblique Space Groups .200 9.3.2 2D Rectangular Space Groups .201 9.3.3 2D Square Space Group .203 9.3.4 2D Hexagonal Space Groups .203 9.4 Line Groups .204 XII Contents 9.5 The Determination of Crystal Structure and Space Group . 205 9.5.1 Determination of the Crystal Structure .206 9.5.2 Determination of the Space Group .206 10 Space Groups in Reciprocal Space and Representations . 209 10.1 Reciprocal Space .210 10.2 Translation Subgroup .211 10.2.1 Representations for the Translation Group .211 10.2.2 Bloch's Theorem and the Basis of the Translational Group .212 10.3 Symmetry of к Vectors and the Group of the Wave Vector . . . 214 10.3.1 Point Group Operation in r-space and fe-space .214 10.3.2 The Group of the Wave Vector Gk and the Star of к . . 215 10.3.3 Effect of Translations and Point Group Operations on Bloch Functions .215 10.4 Space Group Representations .219 10.4.1 Symmorphic Group Representations .219 10.4.2 Nonsymmorphic Group Representations and the Multiplier Algebra .220 10.5 Characters for the Equivalence Representation .221 10.6 Common Cubic Lattices: Symmorphic Space Groups .222 10.6.1 The Г Point .223 10.6.2 Points with к φ 0.224 10.7 Compatibility Relations .227 10.8 The Diamond Structure: Nonsymmorphic Space Group .230 10.8.1 Factor Group and the Γ Point .231 10.8.2 Points with к Φ 0.232 10.9 Finding Character Tables for all Groups of the Wave Vector . . 235 Part V Electron and Phonon Dispersion Relation 11 Applications to Lattice Vibrations .241 11.1 Introduction .241 11.2 Lattice Modes and Molecular Vibrations .244 11.3 Zone Center Phonon Modes .246 11.3.1 The NaCl Structure .246 11.3.2 The Perovskite Structure .247 11.3.3 Phonons in the Nonsymmorphic Diamond Lattice .250 11.3.4 Phonons in the Zinc Blende Structure .252 11.4 Lattice Modes Away from fc = 0.253 11.4.1 Phonons in NaCl at the X Point A- = (тг/о)(100) .254 11.4.2 Phonons in BaTiO3 at the X Point .256 11.4.3 Phonons at the К Point in Two-Dimensional Graphite. 258 Contents XIII 11.5 Phonons in Te and α -Quartz Nonsymmorphic Structures .262 11.5.1 Phonons in Tellurium. 262 11.5.2 Phonons in the α -Quartz Structure .268 11.6 Effect of Axial Stress on Phonons .272 12 Electronic Energy Levels in a Cubic Crystals .279 12.1 Introduction .279 12.2 Plane Wave Solutions at к = 0 .282 12.3 Symmetrized Plane Solution Waves along the Zi- Axis .286 12.4 Plane Wave Solutions at the X Point .288 12.5 Effect of Glide Planes and Screw Axes .294 13 Energy Band Models Based on Symmetry .305 13.1 Introduction .305 13.2 к ■ ρ Perturbation Theory .307 13.3 Example of к ■ ρ Perturbation Theory for a Nondegenerate Г^ Band .308 13.4 Two Band Model: Degenerate First-Order Perturbation Theory .311 13.5 Degenerate second-order к ■ ρ Perturbation Theory .316 13.6 Nondegenerate к ■ ρ Perturbation Theory at a Δ Point .324 13.7 Use of к ■ ρ Perturbation Theory to Interpret Optical Experiments .326 13.8 Application of Group Theory to Valley-Orbit Interactions in Semiconductors .327 13.8.1 Background .328 13.8.2 Impurities in Multivalley Semiconductors .330 13.8.3 The Valley-Orbit Interaction .331 14 Spin-Orbit Interaction in Solids and Double Groups .337 14.1 Introduction .337 14.2 Crystal Double Groups .341 14.3 Double Group Properties .343 14.4 Crystal Field Splitting Including Spin-Orbit Coupling .349 14.5 Basis Functions for Double Group Representations .353 14.6 Some Explicit Basis Functions .355 14.7 Basis Functions for Other Г8+ States .358 14.8 Comments on Double Group Character Tables .359 14.9 Plane Wave Basis Functions for Double Group Representations .360 14.10 Group of the Wave Vector for Nonsymmorphic Double Groups .362 XIV Contents 15 Application of Double Groups to Energy Bands with Spin . 367 15.1 Introduction .367 15.2 E(k) for the Empty Lattice Including Spin-Orbit Interaction . 368 15.3 The к ■ ρ Perturbation with Spin-Orbit Interaction .369 15.4 E (к) for a Nondegenerate Band Including Spin-Orbit Interaction .372 15.5 E (к) for Degenerate Bands Including Spin-Orbit Interaction . 374 15.6 Effective ¿/-Factor .378 15.7 Fourier Expansion of Energy Bands: Slater-Koster Method . . 389 15.7.1 Contributions at d = 0 .396 15.7.2 Contributions at d = 1 .396 15.7.3 Contributions at d = 2 .397 15.7.4 Summing Contributions through d = 2 .397 15.7.5 Other Degenerate Levels .397 Part VI Other Symmetries 16 Time Reversal Symmetry .403 16.1 The Time Reversal Operator .403 16.2 Properties of the Time Reversal Operator .404 16.3 The Effect of Τ on E{k), Neglecting Spin .407 16.4 The Effect of Ť on E{k), Including the Spin-Orbit Interaction .411 16.5 Magnetic Groups .416 16.5.1 Introduction .418 16.5.2 Types of Elements .418 16.5.3 Types of Magnetic Point Groups .419 16.5.4 Properties of the 58 Magnetic Point Groups {A¡.Mk} .419 16.5.5 Exanrples of Magnetic Structures .423 16.5.6 Effect of Symmetry on the Spin Hamiltonian for the 32 Ordinary Point. Groups .426 17 Permutation Groups and Many-Electron States .431 17.1 Introduction .432 17.2 Classes and Irreducible Representations of Permutation Groups .434 17.3 Basis Functions of Permutation Groups .437 17.4 Pauli Principle in Atomic Spectra .440 17.4.1 Two-Electron States .440 17.4.2 Three-Electron States .443 17.4.3 Four-Electron States .448 17.4.4 Five-Electron States .451 17.4.5 General Comments on Manv-Electron States .451 Contents XV 18 Symmetry Properties of Tensors .455 18.1 Introduction .455 18.2 Independent Components of Tensors Under Permutation Group Symmetry .458 18.3 Independent Components of Tensors: Point Symmetry Groups .462 18.4 Independent Components of Tensors Under Full Rotational Symmetry .463 18.5 Tensors in Nonlinear Optics .463 18.5.1 Cubic Symmetry: 0h .464 18.5.2 Tetrahedral Symmetry: T</ .466 18.5.3 Hexagonal Symmetry: D^h .466 18.6 Elastic Modulus Tensor .467 18.6.1 Full Rotational Symmetry: 3D Lsotropy .469 18.6.2 Icosahedral Symmetry .472 18.6.3 Cubic Symmetry .472 18.6.4 Other Symmetry Groups .474 A Point Group Character Tables .479 В Two-Dimensional Space Groups .489 С Tables for 3D Space Groups .499 C.I Real Space .499 C.2 Reciprocal Space .503 D Tables for Double Groups .521 E Group Theory Aspects of Carbon Nanotubes .533 E.I Nanotube Geometry and the (». m) Indices .534 E.2 Lattice Vectors in Real Space .534 E.3 Lattice Vectors in Reciprocal Space .535 E.4 Compound Operations and Tube Helicity .536 E. 5 Character Tables for Carbon Nanotubes .538 F Permutation Group Character Tables .543 References .549 Index .553
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author	Dresselhaus, Mildred S. 1930-2017 Dresselhaus, Gene 1929- Jorio, Ado
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illustrated	Illustrated
index_date	2024-07-02T19:16:03Z
indexdate	2024-07-09T21:09:20Z
institution	BVB
isbn	9783540328971 9783642069451
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016232365
oclc_num	255239464
open_access_boolean
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physical	XV, 582 Seiten Illustrationen
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publisher	Springer
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spelling	Dresselhaus, Mildred S. 1930-2017 Verfasser (DE-588)13388371X aut Group theory application to the physics of condensed matter M. S. Dresselhaus, G. Dresselhaus, A. Jorio Berlin Springer 2008 XV, 582 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Festkörperphysik (DE-588)4016921-2 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Festkörperphysik (DE-588)4016921-2 s DE-604 Dresselhaus, Gene 1929- Verfasser (DE-588)13415603X aut Jorio, Ado Verfasser (DE-588)134156048 aut Erscheint auch als Online-Ausgabe 978-3-540-32899-8 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016232365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Dresselhaus, Mildred S. 1930-2017 Dresselhaus, Gene 1929- Jorio, Ado Group theory application to the physics of condensed matter Gruppentheorie (DE-588)4072157-7 gnd Festkörperphysik (DE-588)4016921-2 gnd
subject_GND	(DE-588)4072157-7 (DE-588)4016921-2
title	Group theory application to the physics of condensed matter
title_auth	Group theory application to the physics of condensed matter
title_exact_search	Group theory application to the physics of condensed matter
title_exact_search_txtP	Group theory application to the physics of condensed matter
title_full	Group theory application to the physics of condensed matter M. S. Dresselhaus, G. Dresselhaus, A. Jorio
title_fullStr	Group theory application to the physics of condensed matter M. S. Dresselhaus, G. Dresselhaus, A. Jorio
title_full_unstemmed	Group theory application to the physics of condensed matter M. S. Dresselhaus, G. Dresselhaus, A. Jorio
title_short	Group theory
title_sort	group theory application to the physics of condensed matter
title_sub	application to the physics of condensed matter
topic	Gruppentheorie (DE-588)4072157-7 gnd Festkörperphysik (DE-588)4016921-2 gnd
topic_facet	Gruppentheorie Festkörperphysik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016232365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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