Group theory and its applications in physics:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German English Japanese |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Edition: | 2., corr. print. |
| Series: | Springer series in solid-state sciences
78 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Japan. übers. |
| Physical Description: | XV, 415 S. graph. Darst. |
| ISBN: | 3540604456 |
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MARC
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| 084 | |a UQ 1350 |0 (DE-625)146479: |2 rvk | ||
| 100 | 1 | |a Inui, Tetsurō |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Ōyō-gunron |
| 245 | 1 | 0 | |a Group theory and its applications in physics |c T. Inui ; Y. Tanabe ; Y. Onodera |
| 250 | |a 2., corr. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a XV, 415 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer series in solid-state sciences |v 78 | |
| 500 | |a Aus d. Japan. übers. | ||
| 650 | 7 | |a Groupes, Théorie des |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 0 | 7 | |a Molekülphysik |0 (DE-588)4039979-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Physik |0 (DE-588)4045956-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Atomphysik |0 (DE-588)4003423-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Gruppentheorie |0 (DE-588)4072157-7 |D s |
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| 689 | 3 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Tanabe, Yukito |e Verfasser |4 aut | |
| 700 | 1 | |a Onodera, Yoshitaka |e Verfasser |4 aut | |
| 830 | 0 | |a Springer series in solid-state sciences |v 78 |w (DE-604)BV000016582 |9 78 | |
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| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1805067441204625408 |
|---|---|
| adam_text |
CONTENTS
SECTIONS
MARKED
WITH
AN
ASTERISK
MAY
BE
OMITTED
ON
A
FIRST
READING.
1.
SYMMETRY
AND
THE
ROLE
OF
GROUP
THEORY
.
1
1.1
ARRANGEMENT
OF
THE
BOOK
.
5
2.
GROUPS
.
7
2.1
DEFINITION
OF
A
GROUP
.
.'
.
7
2.1.1
MULTIPLICATION
TABLES
.
8
2.1.2
GENERATING
ELEMENTS
.
8
*2.1.3
COMMUTATIVE
GROUPS
.
9
2.2
COVERING
OPERATIONS
OF
REGULAR
POLYGONS
.
10
2.3
PERMUTATIONS
AND
THE
SYMMETRIC
GROUP
.
15
2.4
THE
REARRANGEMENT
THEOREM
.
17
2.5
ISOMORPHISM
AND
HOMOMORPHISM
.
18
2.5.1
ISOMORPHISM
.
18
2.5.2
HOMOMORPHISM
.
19
2.5.3
NOTE
ON
MAPPING
.
19
2.6
SUBGROUPS
.
20
*2.7
COSETS
AND
COSET
DECOMPOSITION
.
20
2.8
CONJUGATE
ELEMENTS;
CLASSES
.
21
*2.9
MULTIPLICATION
OF
CLASSES
1
.
23
YY2.10
INVARIANT
SUBGROUPS
.
25
*2.11
THE
FACTOR
GROUP
.
26
*2.11.1
THE
KERNEL
.
28
*2.11.2
HOMOMORPHISM
THEOREM
.
28
2.12
THE
DIRECT-PRODUCT
GROUP
.
28
3.
VECTOR
SPACES
.
31
3.1
VECTORS
AND
VECTOR
SPACES
.
31
*3.1.1
MATHEMATICAL
DEFINITION
OF
A
VECTOR
SPACE
.
31
3.1.2
BASIS
OF
A
VECTOR
SPACE
.
32
3.2
TRANSFORMATION
OF
VECTORS
.
33
3.3
SUBSPACES
AND
INVARIANT
SUBSPACES
.
37
3.4
METRIC
VECTOR
SPACES
.
39
3.4.1
INNER
PRODUCT
OF
VECTORS
.
39
3.4.2
ORTHONORMAL
BASIS
.
39
3.4.3
UNITARY
OPERATORS
AND
UNITARY
MATRICES
.
40
3.4.4
HERMITIAN
OPERATORS
AND
HERMITIAN
MATRICES
.
41
3.5
EIGENVALUE
PROBLEMS
OF
HERMITIAN
AND
UNITARY
OPERATORS
.
41
*3.6
LINEAR
TRANSFORMATION
GROUPS
.
43
XII
CONTENTS
4.
REPRESENTATIONS
OF
A
GROUP
I
.
45
4.1
REPRESENTATIONS
.
45
4.1.1
BASIS
FOR
A
REPRESENTATION
.
47
4.1.2
EQUIVALENCE
OF
REPRESENTATIONS
.
48
4.1.3
REDUCIBLE
AND
IRREDUCIBLE
REPRESENTATIONS
.
48
4.2
IRREDUCIBLE
REPRESENTATIONS
OF
THE
GROUP
C
XV
.
49
4.3
EFFECT
OF
SYMMETRY
TRANSFORMATION
OPERATORS
ON
FUNCTIONS
.
52
4.4
REPRESENTATIONS
OF
THE
GROUP
C
3V
BASED
ON
HOMOGENEOUS
POLYNOMIALS
.
55
4.5
GENERAL
REPRESENTATION
THEORY
.
58
4.5.1
UNITARIZATION
OF
A
REPRESENTATION
.
58
4.5.2
SCHUR
'
S
FIRST
LEMMA
.
59
4.5.3
SCHUR
'
S
SECOND
LEMMA
.
59
4.5.4
THE
GREAT
ORTHOGONALITY
THEOREM
.
59
4.6
CHARACTERS
.
62
4.6.1
FIRST
AND
SECOND
ORTHOGONALITIES
OF
CHARACTERS
.
63
4.7
REDUCTION
OF
REDUCIBLE
REPRESENTATIONS
.
64
4.7.1
RESTRICTION
TO
A
SUBGROUP
.
66
4.8
PRODUCT
REPRESENTATIONS
.
66
4.8.1
SYMMETRIC
AND
ANTISYMMETRIC
PRODUCT
REPRESENTATIONS
.
68
4.9
REPRESENTATIONS
OF
A
DIRECT-PRODUCT
GROUP
.
70
*4.10
THE
REGULAR
REPRESENTATION
.
71
*4.11
CONSTRUCTION
OF
CHARACTER
TABLES
.
72
*4.12
ADJOINT
REPRESENTATIONS
.
74
*4.13
PROOFS
OF
THE
THEOREMS
ON
GROUP
REPRESENTATIONS
.
78
*4.13.1
UNITARIZATION
OF
A
REPRESENTATION
.
78
*4.13.2
SCHUR
'
S
FIRST
LEMMA
.
79
YY4.13.3
SCHUR
'
S
SECOND
LEMMA
.
80
*4.13.4
SECOND
ORTHOGONALITY
OF
CHARACTERS
.
80
5.
REPRESENTATIONS
OF
A
GROUP
II
.
85
*5.1
INDUCED
REPRESENTATIONS
.
85
YY5.2
IRREDUCIBLE
REPRESENTATIONS
OF
A
GROUP
WITH
AN
INVARIANT
SUBGROUP
.
87
*5.3
IRREDUCIBLE
REPRESENTATIONS
OF
LITTLE
GROUPS
OR
SMALL
REPRESENTATIONS
.
90
*5.4
RAY
REPRESENTATIONS
.
93
*5.5
CONSTRUCTION
OF
MATRICES
OF
IRREDUCIBLE
RAY
REPRESENTATIONS
.
-
98
6.
GROUPS
REPRESENTATIONS
IN
QUANTUM
MECHANICS
.
107
6.1
SYMMETRY
TRANSFORMATIONS
OF
WAVEFUNCTIONS
AND
QUANTUM-MECHANICAL
OPERATORS
.
107
6.2
EIGENSTATES
OF
THE
HAMILTONIAN
AND
IRREDUCIBILITY
.
108
CONTENTS
XIII
6.3
SPLITTING
OF
ENERGY
LEVELS
BY
A
PERTURBATION
.
112
6.4
ORTHOGONALITY
OF
BASIS
FUNCTIONS
.
113
6.5
SELECTION
RULES
.
114
*6.5.1
DERIVATION
OF
THE
SELECTION
RULE
FOR
DIAGONAL
MATRIX
ELEMENTS
.
116
6.6
PROJECTION
OPERATORS
.
117
7.
THE
ROTATION
GROUP
.
120
7.1
ROTATIONS
.
120
7.2
ROTATION
AND
EULER
ANGLES
.
122
7.3
ROTATIONS
AS
OPERATORS;
INFINITESIMAL
ROTATIONS
.
124
7.4
REPRESENTATION
OF
INFINITESIMAL
ROTATIONS
.
126
7.4.1
ROTATION
OF
SPIN
FUNCTIONS
.
129
7.5
REPRESENTATIONS
OF
THE
ROTATION
GROUP
.
130
7.6
SU(2),
SO(3)
AND
0(3)
.
134
7.7
BASIS
OF
REPRESENTATIONS
.
135
7.8
SPHERICAL
HARMONICS
.
137
7.9
ORTHOGONALITY
OF
REPRESENTATION
MATRICES
AND
CHARACTERS
.
139
7.9.1
COMPLETENESS
RELATION
FOR
Z
J
(
OJ
)
.
141
7.10
WIGNER
COEFFICIENTS
.
142
7.11
TENSOR
OPERATORS
.
147
7.12
OPERATOR
EQUIVALENTS
.
154
7.13
ADDITION
OF
THREE
ANGULAR
MOMENTA;
RACAH
COEFFICIENTS
.
156
7.14
ELECTRONIC
WAVEFUNCTIONS
FOR
THE
CONFIGURATION
(NL)
X
.
163
7.15
ELECTRONS
AND
HOLES
.
168
7.16
EVALUATION
OF
THE
MATRIX
ELEMENTS
OF
OPERATORS
.
171
8.
POINT
GROUPS
.
176
8.1
SYMMETRY
OPERATIONS
IN
POINT
GROUPS
.
176
8.2
POINT
GROUPS
AND
THEIR
NOTATION
.
178
8.3
CLASS
STRUCTURE
IN
POINT
GROUPS
.
180
8.4
IRREDUCIBLE
REPRESENTATIONS
OF
POINT
GROUPS
.
182
8.5
DOUBLE-VALUED
REPRESENTATIONS
AND
DOUBLE
GROUPS
.
183
8.6
TRANSFORMATION
OF
SPIN
AND
ORBITAL
FUNCTIONS
.
186
*8.7
CONSTRUCTIVE
DERIVATION
OF
POINT
GROUPS
CONSISTING
OF
PROPER
ROTATIONS
.
186
9.
ELECTRONIC
STATES
OF
MOLECULES
.
192
9.1
MOLECULAR
ORBITALS
.
192
9.2
DIATOMIC
MOLECULES:
LCAO
METHOD
.
194
9.3
CONSTRUCTION
OF
LCAO-MO:
THE
ELECTRON
APPROXIMATION
FOR
THE
BENZENE
MOLECULE
.
198
*9.3.1
FURTHER
METHODS
FOR
DETERMINING
THE
BASIS
SETS
.
201
9.4
THE
BENZENE
MOLECULE
(CONTINUED)
.
202
XIV
CONTENTS
9.5
HYBRIDIZED
ORBITALS
.
204
9.5.1
METHANE
AND
SP
3
-HYBRIDIZATION
.
205
9.6
LIGAND
FIELD
THEORY
.
207
9.7
MULTIPLET
TERMS
IN
MOLECULES
.
213
*9.8
CLEBSCH-GORDAN
COEFFICIENTS
FOR
SIMPLY
REDUCIBLE
GROUPS
AND
THE
WIGNER-ECKART
THEOREM
.
221
10.
MOLECULAR
VIBRATIONS
.
230
10.1
NORMAL
MODES
AND
NORMAL
COORDINATES
.
230
10.2
GROUP
THEORY
AND
NORMAL
MODES
.
232
10.3
SELECTION
RULES
FOR
INFRARED
ABSORPTION
AND
RAMAN
SCATTERING
.
237
10.4
INTERACTION
OF
ELECTRONS
WITH
ATOMIC
DISPLACEMENTS
.
238
*10.4.1
KRAMERS
DEGENERACY
.
242
11.
SPACE
GROUPS
.
245
11.1
TRANSLATIONAL
SYMMETRY
OF
CRYSTALS
.
245
11.2
SYMMETRY
OPERATIONS
IN
SPACE
GROUPS
.
246
11.3
STRUCTURE
OF
SPACE
GROUPS
.
248
11.4
BRAVAIS
LATTICES
.
250
11.5
NOMENCLATURE
OF
SPACE
GROUPS
.
253
11.6
THE
RECIPROCAL
LATTICE
AND
THE
BRILLOUIN
ZONE
.
254
11.7
IRREDUCIBLE
REPRESENTATIONS
OF
THE
TRANSLATION
GROUP
.
257
11.8
THE
GROUP
OF
THE
WAVE
VECTOR
K
AND
ITS
IRREDUCIBLE
REPRESENTATIONS
.
259
11.9
IRREDUCIBLE
REPRESENTATIONS
OF
A
SPACE
GROUP
.
264
11.10
DOUBLE
SPACE
GROUPS
.
267
12.
ELECTRONIC
STATES
IN
CRYSTALS
.
272
12.1
BLOCH
FUNCTIONS
AND
E(K)
SPECTRA
.
272
12.2
EXAMPLES
OF
ENERGY
BANDS:
GE
AND
TIBR
.
273
12.3
COMPATIBILITY
OR
CONNECTIVITY
RELATIONS
.
277
12.4
BLOCH
FUNCTIONS
EXPRESSED
IN
TERMS
OF
PLANE
WAVES
.
277
12.5
CHOICE
OF
THE
ORIGIN
.
280
12.5.1
EFFECT
OF
THE
CHOICE
ON
BLOCH
WAVEFUNCTIONS
.
281
12.6
BLOCH
FUNCTIONS
EXPRESSED
IN
TERMS
OF
ATOMIC
ORBITALS
.
.
.
282
12.7
LATTICE
VIBRATIONS
.
284
12.8
THE
SPIN-ORBIT
INTERACTION
AND
DOUBLE
SPACE
GROUPS
.
286
12.9
SCATTERING
OF
AN
ELECTRON
BY
LATTICE
VIBRATIONS
.
287
12.10
INTERBAND
OPTICAL
TRANSITIONS
.
289
12.11
FRENKEL
EXCITONS
IN
MOLECULAR
CRYSTALS
.
291
*12.12
SELECTION
RULES
IN
SPACE
GROUPS
.
296
12.12.1
SYMMETRIC
AND
ANTISYMMETRIC
PRODUCT
REPRESENTATIONS
.
302
CONTENTS
XV
13.
TIME
REVERSAL
AND
NONUNITARY
GROUPS
.
307
13.1
TIME
REVERSAL
.
307
13.2
NONUNITARY
GROUPS
AND
COREPRESENTATIONS
.
310
13.3
CRITERIA
FOR
SPACE
GROUPS
AND
EXAMPLES
.
316
13.4
MAGNETIC
SPACE
GROUPS
.
322
13.5
EXCITONS
IN
MAGNETIC
COMPOUNDS;
SPIN
WAVES
.
324
*13.5.1
SYMMETRY
OF
THE
HAMILTONIAN
.
330
14.
LANDAU
'
S
THEORY
OF
PHASE
TRANSITIONS
.
333
14.1
LANDAU
'
S
THEORY
OF
SECOND-ORDER
PHASE
TRANSITIONS
.
333
14.2
CRYSTAL
STRUCTURES
AND
SPIN
ALIGNMENTS
.
341
*14.3
DERIVATION
OF
THE
LIFSHITZ
CRITERION
.
346
*14.3.1
LIFSHITZ
'
S
DERIVATION
OF
THE
LIFSHITZ
CRITERION
.
349
15.
THE
SYMMETRIC
GROUP
.
351
15.1
THE
SYMMETRIC
GROUP
(PERMUTATION
GROUP)
.
351
15.2
IRREDUCIBLE
CHARACTERS
.
353
15.3
CONSTRUCTION
OF
IRREDUCIBLE
REPRESENTATION
MATRICES
.
355
15.4
THE
BASIS
FOR
IRREDUCIBLE
REPRESENTATIONS
.
358
15.5
THE
UNITARY
GROUP
AND
THE
SYMMETRIC
GROUP
.
360
15.6
THE
BRANCHING
RULE
.
367
15.7
WAVEFUNCTIONS
FOR
THE
CONFIGURATION
(NL)
X
.
370
*15.8
D
IJ
AS
IRREDUCIBLE
REPRESENTATIONS
OF
SU(2)
.
373
*15.9
IRREDUCIBLE
REPRESENTATIONS
OF
U(M)
.
376
APPENDICES
.
378
A.
THE
THIRTY-TWO
CRYSTALLOGRAPHIC
POINT
GROUPS
.
378
B.
CHARACTER
TABLES
FOR
POINT
GROUPS
.
381
ANSWERS
AND
HINTS
TO
THE
EXERCISES
.
392
MOTIFS
OF
THE
FAMILY
CRESTS
.
407
REFERENCES
.
409
SUBJECT
INDEX
.
411 |
| any_adam_object | 1 |
| author | Inui, Tetsurō Tanabe, Yukito Onodera, Yoshitaka |
| author_facet | Inui, Tetsurō Tanabe, Yukito Onodera, Yoshitaka |
| author_role | aut aut aut |
| author_sort | Inui, Tetsurō |
| author_variant | t i ti y t yt y o yo |
| building | Verbundindex |
| bvnumber | BV010564339 |
| classification_rvk | SK 950 UK 3000 UP 1090 UP 1100 UP 1200 UQ 1350 |
| ctrlnum | (OCoLC)468547554 (DE-599)BVBBV010564339 |
| dewey-full | 530.1522 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.152 2 |
| dewey-search | 530.152 2 |
| dewey-sort | 3530.152 12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 2., corr. print. |
| format | Book |
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| id | DE-604.BV010564339 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:34:16Z |
| institution | BVB |
| isbn | 3540604456 |
| language | German English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007043863 |
| oclc_num | 468547554 |
| open_access_boolean | |
| owner | DE-20 DE-384 DE-29T DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-384 DE-29T DE-83 DE-11 DE-188 |
| physical | XV, 415 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in solid-state sciences |
| series2 | Springer series in solid-state sciences |
| spelling | Inui, Tetsurō Verfasser aut Ōyō-gunron Group theory and its applications in physics T. Inui ; Y. Tanabe ; Y. Onodera 2., corr. print. Berlin [u.a.] Springer 1996 XV, 415 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in solid-state sciences 78 Aus d. Japan. übers. Groupes, Théorie des ram Physique mathématique ram Molekülphysik (DE-588)4039979-5 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Atomphysik (DE-588)4003423-9 gnd rswk-swf Festkörperphysik (DE-588)4016921-2 gnd rswk-swf Atomphysik (DE-588)4003423-9 s Gruppentheorie (DE-588)4072157-7 s DE-604 Molekülphysik (DE-588)4039979-5 s Festkörperphysik (DE-588)4016921-2 s Physik (DE-588)4045956-1 s 1\p DE-604 Tanabe, Yukito Verfasser aut Onodera, Yoshitaka Verfasser aut Springer series in solid-state sciences 78 (DE-604)BV000016582 78 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007043863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Inui, Tetsurō Tanabe, Yukito Onodera, Yoshitaka Group theory and its applications in physics Springer series in solid-state sciences Groupes, Théorie des ram Physique mathématique ram Molekülphysik (DE-588)4039979-5 gnd Gruppentheorie (DE-588)4072157-7 gnd Physik (DE-588)4045956-1 gnd Atomphysik (DE-588)4003423-9 gnd Festkörperphysik (DE-588)4016921-2 gnd |
| subject_GND | (DE-588)4039979-5 (DE-588)4072157-7 (DE-588)4045956-1 (DE-588)4003423-9 (DE-588)4016921-2 |
| title | Group theory and its applications in physics |
| title_alt | Ōyō-gunron |
| title_auth | Group theory and its applications in physics |
| title_exact_search | Group theory and its applications in physics |
| title_full | Group theory and its applications in physics T. Inui ; Y. Tanabe ; Y. Onodera |
| title_fullStr | Group theory and its applications in physics T. Inui ; Y. Tanabe ; Y. Onodera |
| title_full_unstemmed | Group theory and its applications in physics T. Inui ; Y. Tanabe ; Y. Onodera |
| title_short | Group theory and its applications in physics |
| title_sort | group theory and its applications in physics |
| topic | Groupes, Théorie des ram Physique mathématique ram Molekülphysik (DE-588)4039979-5 gnd Gruppentheorie (DE-588)4072157-7 gnd Physik (DE-588)4045956-1 gnd Atomphysik (DE-588)4003423-9 gnd Festkörperphysik (DE-588)4016921-2 gnd |
| topic_facet | Groupes, Théorie des Physique mathématique Molekülphysik Gruppentheorie Physik Atomphysik Festkörperphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007043863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016582 |
| work_keys_str_mv | AT inuitetsuro oyogunron AT tanabeyukito oyogunron AT onoderayoshitaka oyogunron AT inuitetsuro grouptheoryanditsapplicationsinphysics AT tanabeyukito grouptheoryanditsapplicationsinphysics AT onoderayoshitaka grouptheoryanditsapplicationsinphysics |