Group theory and its applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford, U. K.
Alpha Science International Ltd.
[2018]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 194 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9781842659472 |
Internformat
MARC
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| 020 | |a 9781842659472 |9 978-1-84265-947-2 | ||
| 035 | |a (OCoLC)1018239617 | ||
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| 100 | 1 | |a Patra, P. K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Group theory and its applications |c P. K. Patra, R. K. Thapa |
| 264 | 1 | |a Oxford, U. K. |b Alpha Science International Ltd. |c [2018] | |
| 300 | |a ix, 194 Seiten |b Illustrationen, Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1804178198165979136 |
|---|---|
| adam_text | Contents
Preface
V
1. INTRODUCTION 1.1—1.36
1.1 Introduction 1.1
1.2 Symmetry 1.4
1.2.1 Symmetry Operations 1.5
1.2.2 Symmetry Elements 1.7
1.2.3 Symmetry Operations and Symmetry Elements 1.7
1.2.4 Total Number of Symmetry Operations in a Molecule 1.27
1.2.5 Products of Symmetry Operations and Multiplication Table 1.32
1.2.6 Applications of Symmetry 1.34
Exercises 1.36
2. GROUP THEORY 2.1—2.92
2.1 Groups 2.1
2.2 Point Groups and their Symmetry Elements 2.3
2.2.1 Non-rotational Point Groups 2.4
2.2.2 Single-Axis Rotational Point Groups 2.4
2.2.3 Dihedral Point Groups 2.8
2.2.4 Cubic Point Groups 2.12
2.3 Symmetry Transformations of an Equilateral Triangle and a Square 2.14
2.4 Generating Elements of a Point Group 2.19
2.5 Some Special Groups 2.19
2.5.1 Cyclic Groups 2.19
2.5.2 Permutation Group 2.20
2.5.3 Matrix Groups 2.22
2.6 Subgroups 2.23
2.7 Cosets 2.24
2.8 Conjugate Elements 2.26
Contents
2.9 Class of a Group 2.28
2.9.1 Product of Two Classes 2.31
2.10 Normal Subgroups and Factor Groups 2.31
2.11 Isomorphism and Homomorphism 2.33
2.12 Representation of Groups 2.36
2.12.1 Equivalent Representations 2.38
2.12.2 Unitary Representations 2.39
2.12.3 Reducible and Irreducible Representations 2.40
2.12.4 Relationship between Reducible and Irreducible
Representations 2.42
2.12.5 Reducibility of a Representation 2.42
2.12.6 Characters of a Representation 2.46
2.13 Generating Representations and its Character 2.47
2.13.1 One-dimensional Representations 2.48
2.13.2 Representations of Dimensions Greater than one
for Symmetry Operators 2.60
2.13.3 Two-Dimensional Representations 2.65
2.13.4 Three-dimensional Representations and its Characters 2.68
2.14 Reducible Representations for Molecules 2.74
2.14.1 Contributions to Character of Symmetry Operations
per Unshifted Atom 2.79
2.14.2 Character of Reducible Representations for Molecules
and Ion 2.81
2.15 Representation and Character Vectors 2.82
2.15.1 Representation Vectors 2.82
2.15.2 Character Vectors 2.83
2.15.3 Properties of Representation and Character Vectors 2.84
2.16 The Great Orthogonality Theorem 2.86
2.17 Regular Representation 2.87
Exercises 2.89
3. CHARACTER TABLES FOR POINT GROUPS 3.1—3,18
3.1 Rules for Construction of Character Tables of a Point Group 3.1
3.2 Construction of Character Tables of a Few Point Groups 3.3
3.2.1 The Character Table for the C2v Point Group 3.3
3.2.2 The Character Table for the C3v Point Group 3.6
3.2.3 The Character Table for the C4v Point Group 3.7
Contents
3.3 Rules for Labelling of Irreducible Representations 3.9
3.3.1 Symbols A and B 3.9
3.3.2 Other Symbols 3.10
3.4 Reduction of Reducible Representation of a Point Group 3.12
3.5 Procedure to Study Character Tables 3.13
Exercises 3.16
4. BASIS FUNCTIONS BY USING PROJECTION
OPERATOR METHOD 4.1—4.14
4.1 Basis Functions for Irreducible Representations 4.1
4.2 Application of Projection Operator Method of Group Theory
to Deduce Basis Functions 4.3
4.2.1 Derivation of Basis Functions from an Arbitrary Function 4.3
4.2.2 Derivation of the Basis Function for the Surface State 4.11
Exercises 4.14
5. APPLICATIONS OF GROUP THEORY 5.1—5.18
5.1 Free Electron Energy Bands with Labelling 5.1
5.2 Applications of Group Theory to Semiconductors Optics 5.15
Exercises 5.18
References R.l—R.2
Index LI—1.4
|
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| id | DE-604.BV044715123 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:00:09Z |
| institution | BVB |
| isbn | 9781842659472 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030111566 |
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| physical | ix, 194 Seiten Illustrationen, Diagramme 24 cm |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Alpha Science International Ltd. |
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| spelling | Patra, P. K. Verfasser aut Group theory and its applications P. K. Patra, R. K. Thapa Oxford, U. K. Alpha Science International Ltd. [2018] ix, 194 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Thapa, R. K. Verfasser aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030111566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Patra, P. K. Thapa, R. K. Group theory and its applications Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 |
| title | Group theory and its applications |
| title_auth | Group theory and its applications |
| title_exact_search | Group theory and its applications |
| title_full | Group theory and its applications P. K. Patra, R. K. Thapa |
| title_fullStr | Group theory and its applications P. K. Patra, R. K. Thapa |
| title_full_unstemmed | Group theory and its applications P. K. Patra, R. K. Thapa |
| title_short | Group theory and its applications |
| title_sort | group theory and its applications |
| topic | Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030111566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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