![post-title](https://i.ytimg.com/vi/_RsaNzZFuUU/hqdefault.jpg)
c3v character table 在 コバにゃんチャンネル Youtube 的精選貼文
![post-title](https://i.ytimg.com/vi/_RsaNzZFuUU/hqdefault.jpg)
Search
... <看更多>
... <看更多>
#1. Character table for point group C3v
Character table for point group C ; A · +1, +1, -1, R ; E · +2, -1, 0, (x, y) (Rx, Ry) ...
#4. 3_4 Character tables - Chemistry |
Deriving character tables: Where do all the numbers come from? • A general and rigorous method for ... let's check that with the C3v character table above:.
#5. 1 Rz E 2 -1 0 (x
Symmetry, Point Group s and Character Tables. Character Table for C3v ... In any given representation the characters of all matrices.
#6. Character table for the C 3v point group - Gernot Katzer
Character table for the symmetry point group C3v as used in quantum chemistry and spectroscopy, with an online form implementing the Reduction Formula for ...
#7. Point Group Symmetry Character Tables - c3v
c3v - Point Group Symmetry Character Tables. ... Character table for C3v point group ... Product table for C3v point group ...
#8. Definition C3 v is the symmetry group of an equilateral triangle ...
This is the same as the multiplication table for the cyclic group C2 e, C2 . Therefore ... Note that C3 h is abelian & isomorphic to C6. 2. C3v.nb ...
#9. Character Tables
Character tables contain information about how functions transform in response to the ... The C3v Character Table: Definition of “Character”.
under the symmetry operations of the C3v point group. The act of each of the six ... In similar fashion, the C3v character table states that dx2−y.
#11. Point Group C3v - an overview | ScienceDirect Topics
The multiplication table, shown in Table 4.1, can be constructed. Table 4.1. Multiplication Order of Symmetry. C3v, E, C ...
#12. 1.14: Character Tables - Chemistry LibreTexts
2021年12月5日 — 1.14: Character Tables · The first element in the table gives the name of the point group, usually in both Schoenflies (C3v) and Hermann-Mauguin ...
#13. Construction of C3V character table - SlideShare
C3v SYMMENTRY OPERATIONS NH3 C3v Point group contains symmentry elements of ORDER of the. CONSTRUCTING CHARACTER TABLE IS FOLLOWED BY 4 STEPS through ...
#14. Symmetry point group
Explain: using C3v character table. Construction of character tables: C2v: Four nonredundant symmetry operations and each is in a separate class ...
#15. Trigonal: C3v - University of Exeter
sm_C3v stereograph · C3v solid · NH3 · Stereograph · 3D object · Molecule NH3 (Ammonia). C3v correlation table · C3v product tables ...
#16. Irreducible Representations and Character Tables
Representations and Character. Tables. 9. Example: C3v {E, C3. +, C3. -, σa, σb, σ3} defined w.r.t. the xz plane y x a b c. -π/3. +π/3. C734b Irreducible.
#17. Tables for Group Theory
This provides the essential tables (character tables, direct products, ... C2, C3, C6, D3, D6, C2v, C3v, C6v, C2h, C3h, C6h, D3h, D6h, D3d, S6.
#18. Operations of C3v Symmetry Group Applied to Ammonia
... of successive symmetry operations of the group applied to the ammonia molecule and how this corresponds to the multiplication table of ...
#19. chapter 12 - molecular symmetry
The. C3v character table reveals that NH3, and other molecules of the same symmetry, can have only nondegenerate and two-fold degenerate energy levels. The ...
#20. Group theory
The multiplication table of the C2v point group with four symmetry operations (E, Cz ... Table 4.2: Multiplication table of the C3v point group.
#21. CHAPTER 4: SYMMETRY AND GROUP THEORY
including one hydrogen and all three C's. C3v. d. 3-Chloropropene (assuming a rigid molecule, ... Character Table: C3v. E 2 C3. 3 σv. Matching Functions.
#22. Symmetry: Translation and Rotation
character table indicates the ... The seventh column of the table contains the symmetry ... The C3v. Character Table. Some differences from C2v.
#23. 1 Rz xy 1
Characters of the irreducible representation. │. │. │. ⎠. ⎞. │ ... Chem 104A, UC, Berkeley. Properties of Character Table. C3v. E. 2C3. 3σv. A1. 1. 1.
#24. Solved For the C3v character table below, A2 obeys the - Chegg
Show then that A2 and E obey the character table rule that any two irreducible representation sets must be orthogonal to each other. C3v E203 30 Linear (z) ...
#25. I. Symmetry and Group Theory in Chemistry - Dr. Shyama ...
representation of groups, The defining property of a group, Sub group and Class, Group multiplication table for C2V, C2h and C3V point group, Generators and ...
#26. Point Group C3v - Quanty
E · (1) ; (2) ; (3) ...
#27. On the character and conjugacy classes of C3v point group ...
orthogonality theorem, we reduced the blocked diagonal matrix to its irreducible form to get the character table. The character table thus.
#28. The character table for a pyramidal AB3 molecule of C3v point ...
The character table for a pyramidal AB3 molecule of C3v point group is given below: C3v E 2C3 3σv A1 ... 3E 3. 3A1 + A2 + E 4. 2A1 + 2E 5.
#29. A Point Group Character Tables
Table C.22. Character table with point group symmetry C3v (3m) for group of the wave vector for a point Λ for the space group #166 R¯3m. C3v(3m).
#30. The character table for a pyramidal AB 3 molecule of C 3v ...
Therefore, IR active modes will be Raman inactive and vice-versa. Calculation: Given: The character table is given as follows: C3v.
#31. GROUP THEORY AND ITS APPLICATIONS
Multiplication Table for Symmetry Operations of NH3 molecule i.e., for C3v. Point Group. Symmetry operations. NH3 (C3v). E. C3. 1. C3.
#32. What is the character table of C3v point group? - Wherevermag
Character table for point group C3v ... In a given representation (reducible or irreducible), the characters of all matrices belonging to symmetry ...
#33. Character table - Wikipedia
In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, ...
#34. A chemist's view of group theory
Getting back to our C3v character table, the characters for any given irreducible representation must be the same for operations in the same class.
#35. Applications of molecular symmetry and group theory - e-PG ...
How to find Γvib for C2v,C3v,Td,D4h point groups. 2. Introduction ... The character table in part for D4h point group together with T3N is given in Table .1.
#36. File:C3v Character Table.jpg - Wikimedia Commons
File:C3v Character Table.jpg. No higher resolution available. C3v_Character_Table.jpg (362 × 76 pixels, file size: 14 KB, ...
#37. Group theory in action: molecular vibrations
unshifted atoms and the contribution to character. C2v. E. 2. C. V ... C3v. E. C3. C3. 2 σv ... 3. μ : character table, x→B1, y→B2, z→A1 τ ψ τ μψ ψ τ ψ ψ.
#38. 3 4 character tables - PDFSLIDE.NET
In C3v there are three classes and hence three irreducible representations. 77. 2) The characters of all operations in the same class are equal in each given ...
#39. Introduction to Group Theory
isomorphism between permutation group P3 and symmetry group C3v of ... d d f c b e a. f f c d a b e. Character table. P3 e a, b c, d, f. C3v.
#40. Degenerate Representations - Hunt Research Group
under the symmetry operations of the C3v point group. E. C3v. 2C3. 3σv. 1 1 1. A1. 1 1 -1. A2. 2 -1 0. E. (Tx, Ty). Tz. C3v character table.
#41. Chapter 5 - Holooly.com
Constructing a character table. Use the restrictions derived above and the LOT to complete the C 3 v C_{3\text {v}} C3v character table.
#42. If
Character table of C3v point group is given below 1 point 1 point E ... Point Group s and Character Tables Character Table for C3v E2C3 3) v A1 11 1z x 2 + ...
#43. Point Group Tables - Bilbao Crystallographic Server
Character Table. Point Subgroups. Multiplication Table of Irreps. Irreps Decompositions of important (ir)rreps. Infrared and Raman Selection Rules. The Rotation ...
#44. A Point Group Character Tables
Appendix A contains Point Group Character (Tables A.1–A.34) to be used ... Character table for group C3v (rhombohedral). C3v (3m).
#45. [問題] 群論... - 精華區Chemistry - 批踢踢實業坊
S4的character table會出現i S6的character table會出現ε 簡單的character table可以用湊的,但是複雜的又該如何呢? C3v │E 2C3 3σv│ ...
#46. Part 2.5: Character Tables - ppt video online download
Review Character table structure Properties of Char. Tables Mulliken symbols Order ... 43 From the Rules: C3v Classes are grouped. The table is square.
#47. Review of Matrices
L The character of a matrix (symbol chi, χ) is the sum of the ... More Complex Groups and. Standard Character Tables. C3v. E 2C3 3σv.
#48. Appendix 12: Character Tables - Wiley Online Library
Character Tables. This appendix lists the standard character tables for the point groups met in the main text. The right-hand columns indicate the ...
#49. Chem 59-250 Character Tables for Point Groups
that are conveniently listed as a matrix known as a Character Table. As an example, we will look at the character table for the C. 2v point group.
#50. Molecular Symmetry
two σv vertical planes, σv, and σv associated with two mirror reflections. 6. Page 7. TABLE I: Multiplication Table for the C3v Group. E.
#51. Character Tables: Irreps Symbols - CEM311 - Lecture Slides
An illustration showing that the maximum degeneracy in NH3 is also 2. (C3v point group: px and py are equivalent, but pz is not). Fig. 6.13. Example 6.4 (p.195):.
#52. Character Tables - StudyLib
3 Character Table Group Symbol Irreducible Representations Symmetry Elements Characters ... 41 From the Rules: C2v A1 A2 B1 B2 42 From the Rules: C3v 1.
#53. 2018 Ch112 − Problem Set 2 Due: Thursday, October 25
1) For molecules A and B, list the symmetry operations and point groups. Consider the following multiplication table for C3v, filled in ...
#54. Symmetry and Group Theory - C2v and C3v - Free Video ...
Lecture 30 : Character Tables: C2v and C3v tutorial of Symmetry and Group Theory course by Prof Prof. Anindya Datta of IIT Bombay.
#55. Polyatomic molecules_1.pdf - UConn Physics
Note that the C3v character table lists only the classes, not all six individual symmetry operators, because the irreducible representations and characters ...
#56. On the Character and Conjugacy Classes of C3v Point Group ...
Keyword: Conjugacy Classes, Point Groups, Orthogonality, Character Table, Irreducible, Symmetry Elements. 1. Introduction. The classification of molecules ...
#57. What is character symmetry table? - Greedhead.net
Character table for point group C3v. C3v, E, cubic functions. A1, +1, z3, x(x2-3y2), z(x2+y2).
#58. a) b) c) d) e) f) g) k) h) l)
Lets say we have a reducible representation Γred in C3v which is given below: ... Character table: Γx,y has the same characters as the E representation,.
#59. Grouping of symmetry classes in chemistry character tables
The σv mirror planes in the C3v point group are themselves related by symmetry: note that they can be interchanged via rotation by 120 ...
#60. MODEL ANSWER
From character table we see that… Γtrans = E' + A2” ... From character tables we see that only E' will be visible in both IR and Raman spectra.
#61. QUESTION BANK CHP -4102 Section I
b) C3v c) Oh d) D3h. 3) Point group of Cyclohexane is - a) Chair form is D3d ... 5) The character table for C2v point group is given below. In cis butadiene.
#62. 3 4 character tables - [PDF Document] - Cupdf
In C3v there are three classes and hence three irreducible representations. 77. 2) The characters of all operations in the same class are equal ...
#63. Ammonia C3V - ChemTube3D
Ammonia belongs to the C3v Point group and contains;one C3 rotation axis along with 3σv planes of symmetry. Pointgroup Flow Chart.
#64. A Point Group Character Tables - UCSD Physics
Appendix A contains Point Group Character (Tables A.1–A.34) to be used ... Character table for group C3v (rhombohedral). C3v (3m).
#65. How do you create a character table in group theory?
The C3v point group is isomorphic to D3. It is also isomorphic to the Symmetric Group Sym(3), the group of all ...
#66. Group Theory Mini-Exam
(14 pts) The reducible representation in Question 4 represents all 3N molecular motions in ammonia, NH3. Please use the C3v character table and the irreducible ...
#67. Group Theory - ASA
These Operations Are Given In The Top Row Of The Character Table. ... σv">σvσv leads To C3v">C3vC3v point Group, Which Leads To The C3v Character Table.
#68. How to build Character Tables - All 'Bout Chemistry
a character table is a two-dimensional table whose rows correspond to ... In The Similar Way You can Make Character Table for C3V
#69. E–1402
C3v point group ? 3. Construct a character table for C2v point group. Assign. Mulliken's symbols to the irreducible representations.
#70. Group Theory - Genesis Tutorials
Coloumn I:- Its Coloumn of character table shows mullein symbol for irreducible representation of the group. IR1. 1. 1. 1. IR2. 1. 1. -1. IR3. 2. 3 m3. C3v.
#71. notes01 - Symmetry, Point Group s and Character Tables...
View Notes - notes01 from CHEM 204 at Johns Hopkins University. Symmetry, Point Group s and Character Tables Character Table for C3v E 2C3 3 )v A1 1 1 1 z ...
#72. Group Theory for Chemists Fundamental ... - Passei Direto
Thus, the table of irreducible representations for C3v can be re-written as: ... can therefore be simplified further as: Table 2.3 The C3v character table.
#73. σv σv σv - FIU Faculty Websites
One can see that pxzpz spans E. Therefore, the integral is necessarily zero. 4. The C3v character table: C3v. E. 2C3. 3σv.
#74. Point-Group Theory Tables - Theoretical Chemistry
Obtention of the character table for the double group ... C3v subgroups and subduction can only be ensured for two of them at the same time. (This is not an.
#75. II UNIT – III Fundamentals of Group Theory
group,group multiplication table for C2V and C3V point groups-- matrix representation of symmetry operations and transformation matrices ––– representation ...
#76. MOLECULAR SYMMETRY - Chemistry Division, Faculty of ...
Character tables and symmetry labels ... Character Table is a table that characterizes the ... The Structure of Character Tables. C3v.
#77. H bonds in the ammonia molecule is C3v E 2C3 30v A1 1 A2 ...
Given the C3v character table below, the reducible representation (C) for the three N- H bonds in the ammonia molecule is C3v E 2C3 30v A1 1 A2 1 E 2 a) 3 1 0 b ...
#78. 3 4 Character tables - Home - University of Character ta76 3.4 ...
In C3v there are three classes and hence three irreducible representations. 77. 2) The characters of all operations in the same class are equal ...
#79. Chapter 5 Characters and Character Tables
Characters and Character. Tables. In great mathematics there is a very high degree ... acter table for S3, which is known as the group C3v when interpreted.
#80. Polyatomic Molecular Orbital Theory - La Salle University
from corresponding character tables by their inspection holding in mind the ... the character table of C3v a1 + e. 2) Molecular Orbitals of NH3 (C3v). C3v.
#81. Lecture Notes on Molecular Symmetry and Group Theory
... of Groups Character Tables and Their Applications References Carter… ... by inspection to give irreducible representation character table C3v E 2C3 3&v ...
#82. Group theory and the classification of elementary excitations ...
Table 2: Multiplication tables of the groups C3 and C3. C3v, the so-called right cosets by multiplying all elements of the subgroup H of G with a fixed element ...
#83. Properties of Nitrogen-Vacancy Centers in Diamond
The spin character of the defect will be determined by the degeneracy of the orbitals and ... TABLE IV: Character and bases table for the double C3v group.
#84. Chapter 4
The character, χ, of a matrix is equal to the sum of its diagonal ... preceding the operations on the top line of the character table. C3v E 2C3 3σv.
#85. Mathematical Physics 18KP1P01
In group theory, a branch of abstract algebra, a character table is a two- dimensional table whose rows ... Group multiplication table for C3v for Ammonia ...
#86. 4 Molecular Symmetry - NET
tations for the C3v point group. ... character table of the C2h point group is shown below. ... tries: (i) C1; (ii) C2; (iii) Cs; (iv) C2h; (v) C3v.
#87. Applications of Group Theory to the Physics of Solids
15.4 Character Tables for Groups of the Wave Vector . . . . . 434 ... symmetry group is C3v, and the character table is given in Table 8.2.
#88. Character Table Point Group - Never Stop Learning
Synthesize all learning information about Character Table Point Group and related news to help ... (ENGLISH) CHARACTER TABLES FOR C2V & C3v POINT GROUP.
#89. Molecular symmetry - Lund University Publications
table form in order to generate projection operations for the irreducible representations. These tables are called character tables, and the C3v character.
#90. 1 EXPERIMENT 5 MOLECULAR SYMMETRY, POINT ...
MOLECULAR SYMMETRY, POINT GROUPS AND CHARACTER TABLES. NOTE: lab write-up consists of submitting ... Therefore NH3 must have C3v symmetry. SYMMETRY GROUPS.
#91. Practical Group Theory and Raman Spectroscopy, Part I
Here we use the ammonia molecule NH3 of point group C3v to understand the role of degeneracy in spectra. The character table for the. C3v point group is shown ...
#92. Symmetries On The Lattice
The group C3v has three conjugate classes: ... The Character χR (g) of g ∈ G in a given R representation is ... Characters table : C3v.
#93. Group Theory Formula Sheet
Gibbs Free energyhange. Componenets of character table. Page 12. Gibbs Free energyhange. Character table of C2v point gp. Character table of C3v point gp.
#94. Molecular vibrations - CAMD
Reduction of Γ using character table of C3v. C3v ... Think of rows in the above table as vectors. ▻ Then Γ=3A1 + A2 + 4E.
#95. Character Tables
1, IR of C3v species: 2, 1. Draw Cartesian axes on each ligand parallel to main Cartesian System. 3, To avoid the work of writing 12x12 transformation ...
#96. (PPT) Chapter 5 sym and Gr Thy | guesh g/selassie
C3 C3v D4d D4h 3-fold rotational has σv but 4-fold d = no 'h' indicates 32 axis no ... The character table lists all of the symmetry elements of the group, ...
#97. What is the purpose of a character table biology? - Best Acting ...
... of the possible irreducible representations of a group under each of the symmetry operations of the group. The character table for C3v is shown below.
c3v character table 在 [問題] 群論... - 精華區Chemistry - 批踢踢實業坊 的推薦與評價
C3v │E 2C3 3σv
──┼──────
A1 │1 1 1
A2 │1 -1 1
E │2 -1 0
想問~是如何決定上述的數字壓?
應該是先決定數字才能判斷A1 A2吧...
數字1 -1 2 0再這代表什麼意義壓?
我還是搞不懂...
有迷有人可以告訴我 Q_Q
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: sunev (不知所謂) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Sun Nov 2 22:21:21 2003
※ 引述《vicianose ( )》之銘言:
: C3v │E 2C3 3σv
: ──┼──────
: A1 │1 1 1
: A2 │1 -1 1
1 1 -1
: E │2 -1 0
: 想問~是如何決定上述的數字壓?
就我目前學到的知識
用湊的...^^;;
: 應該是先決定數字才能判斷A1 A2吧...
沒錯...
: 數字1 -1 2 0再這代表什麼意義壓?
: 我還是搞不懂...
: 有迷有人可以告訴我 Q_Q
^^ (u和o有點遠?)
你得先了解什麼是representation
representation正如其名
是一種表達operator的方式
最一般的做法是拿xyz來做成矩陣
可以想像
representation的取法有無限多種
但數學家告訴我們
所有的representation都可以表為少數幾個
irreducible representation的線性組合
而下面的那些數字就是所謂的irreducible repersentation.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 210.85.226.46
> -------------------------------------------------------------------------- <
作者: vicianose ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Sun Nov 2 22:41:55 2003
※ 引述《sunev (不知所謂)》之銘言:
: ※ 引述《vicianose ( )》之銘言:
: : C3v │E 2C3 3σv
: : ──┼──────
: : A1 │1 1 1
: : A2 │1 -1 1
: 1 1 -1
^^^^^^^^^^^
???????????????
: : E │2 -1 0
: : 想問~是如何決定上述的數字壓?
: 就我目前學到的知識
: 用湊的...^^;;
: : 應該是先決定數字才能判斷A1 A2吧...
: 沒錯...
: : 數字1 -1 2 0再這代表什麼意義壓?
: : 我還是搞不懂...
: : 有迷有人可以告訴我 Q_Q
: ^^ (u和o有點遠?)
: 你得先了解什麼是representation
: representation正如其名
: 是一種表達operator的方式
: 最一般的做法是拿xyz來做成矩陣
: 可以想像
: representation的取法有無限多種
: 但數學家告訴我們
: 所有的representation都可以表為少數幾個
: irreducible representation的線性組合
: 而下面的那些數字就是所謂的irreducible repersentation.
我看後面其他的character table
譬如說...S4的character table會出現i
S6的character table會出現ε
簡單的character table可以用湊的,但是複雜的又該如何呢?
C3v │E 2C3 3σv│ │
──┼──────┼───────┼───────────
A1 │1 1 1 │z │x^2+y^2, z^2
A2 │1 -1 1 │Rz │
E │2 -1 0 │(x,y) (Rx,Ry) │ (x^2-y^2,xy) (xy,yz)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
不知這又怎麼出來的~Q__Q~
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: sunev (不知所謂) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Sun Nov 2 23:18:35 2003
※ 引述《vicianose ( )》之銘言:
: ※ 引述《sunev (不知所謂)》之銘言:
: : 1 1 -1
: ^^^^^^^^^^^
: ???????????????
我是用背的...
我記錯了嗎?? ^^;;
: : 但數學家告訴我們
: : 所有的representation都可以表為少數幾個
: : irreducible representation的線性組合
: : 而下面的那些數字就是所謂的irreducible repersentation.
: 我看後面其他的character table
: 譬如說...S4的character table會出現i
: S6的character table會出現ε
ε 和 i其實意謂著同一件事
就是複數的出現
好像可交換群就是會生出這種東西
Cn也是
詳細狀況我也不清楚...:p
: 簡單的character table可以用湊的,但是複雜的又該如何呢?
: C3v │E 2C3 3σv│ │
: ──┼──────┼───────┼───────────
: A1 │1 1 1 │z │x^2+y^2, z^2
: A2 │1 -1 1 │Rz │
: E │2 -1 0 │(x,y) (Rx,Ry) │ (x^2-y^2,xy) (xy,yz)
: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
: 不知這又怎麼出來的~Q__Q~
把後面的函數當成一種representation
去算其代表各operator的
就會發現這個函數的representation
恰好就是這個row的irreducible representation
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 210.85.226.46
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Mon Nov 3 22:45:46 2003
※ 引述《vicianose ( )》之銘言:
: C3v │E 2C3 3σv
: ──┼──────
: A1 │1 1 1
: A2 │1 -1 1
: E │2 -1 0
: 想問~是如何決定上述的數字壓?
: 應該是先決定數字才能判斷A1 A2吧...
: 數字1 -1 2 0再這代表什麼意義壓?
: 我還是搞不懂...
: 有迷有人可以告訴我 Q_Q
一定有個 total symmetric 的representation, 所以 A1 的就不說啦,
假設為 A2 為 a1 a2 a3
E 為 b1 b2 b3
則由 a1^2 + 2*a2^2 + 3*a3^2 = 6 (6為order =1+2+3)
應該不難湊出整數解了, 可以 a1*1 + a2*1 + a3*1 是否等於 0 確認,
a1 a2 a3 是算對;
再由
b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
即可求出 b1 b2 b3
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.118
> -------------------------------------------------------------------------- <
作者: vicianose ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Tue Nov 4 14:16:04 2003
※ 引述《barts ( )》之銘言:
: ※ 引述《vicianose ( )》之銘言:
: : C3v │E 2C3 3σv
: : ──┼──────
: : A1 │1 1 1
: : A2 │1 -1 1
: : E │2 -1 0
: : 想問~是如何決定上述的數字壓?
: : 應該是先決定數字才能判斷A1 A2吧...
: : 數字1 -1 2 0再這代表什麼意義壓?
: : 我還是搞不懂...
: : 有迷有人可以告訴我 Q_Q
: 一定有個 total symmetric 的representation, 所以 A1 的就不說啦,
: 假設為 A2 為 a1 a2 a3
: E 為 b1 b2 b3
: 則由 a1^2 + 2*a2^2 + 3*a3^2 = 6 (6為order =1+2+3)
: 應該不難湊出整數解了, 可以 a1*1 + a2*1 + a3*1 是否等於 0 確認,
: a1 a2 a3 是算對;
: 再由
: b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: 即可求出 b1 b2 b3
你的意思是說 b1 b2 b3各為 2 1 0 嗎??
但是這樣1*b1*1+2*b2*1+3*b3*1就會不=0耶...^^a
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Tue Nov 4 19:16:39 2003
※ 引述《vicianose ( )》之銘言:
: ※ 引述《barts ( )》之銘言:
: : 一定有個 total symmetric 的representation, 所以 A1 的就不說啦,
: : 假設為 A2 為 a1 a2 a3
: : E 為 b1 b2 b3
: : 則由 a1^2 + 2*a2^2 + 3*a3^2 = 6 (6為order =1+2+3)
: : 應該不難湊出整數解了, 可以 a1*1 + a2*1 + a3*1 是否等於 0 確認,
: : a1 a2 a3 是算對;
: : 再由
: : b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: : 即可求出 b1 b2 b3
: 你的意思是說 b1 b2 b3各為 2 1 0 嗎??
: 但是這樣1*b1*1+2*b2*1+3*b3*1就會不=0耶...^^a
所以 2 1 0 是錯的, 2 -1 0 才對
1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.137
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Tue Nov 4 19:26:23 2003
※ 引述《vicianose ( )》之銘言:
: ※ 引述《sunev (不知所謂)》之銘言:
: : 1 1 -1
: ^^^^^^^^^^^
: ???????????????
: : 就我目前學到的知識
: : 用湊的...^^;;
: : 沒錯...
: : ^^ (u和o有點遠?)
: : 你得先了解什麼是representation
: : representation正如其名
: : 是一種表達operator的方式
: : 最一般的做法是拿xyz來做成矩陣
: : 可以想像
: : representation的取法有無限多種
: : 但數學家告訴我們
: : 所有的representation都可以表為少數幾個
: : irreducible representation的線性組合
: : 而下面的那些數字就是所謂的irreducible repersentation.
: 我看後面其他的character table
: 譬如說...S4的character table會出現i
: S6的character table會出現ε
: 簡單的character table可以用湊的,但是複雜的又該如何呢?
: C3v │E 2C3 3σv│ │
: ──┼──────┼───────┼───────────
: A1 │1 1 1 │z │x^2+y^2, z^2
: A2 │1 -1 1 │Rz │
: E │2 -1 0 │(x,y) (Rx,Ry) │ (x^2-y^2,xy) (xy,yz)
: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
: 不知這又怎麼出來的~Q__Q~
沒錯, 簡單可以用湊的, 複雜的(非整數)很難算;
所以一般都不會考太難的, 如 Cnv, Dnh, Td, 考到Td就已經是殘忍了,
如果考 Oh 以上就沒人性啦~~~~~
至於你指的第III, IV區, 還是可以算出來, 不過, 在這很難跟你解釋;
運氣好的話, 無機會提到, 不然要等研究所的高等無機才會教!!
有興趣可參考 F.A. cotton application of group theory (書名快忘了)!!
寫得不錯, 不過第一次念不容易懂唷~~~~
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.137
> -------------------------------------------------------------------------- <
作者: vicianose ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Wed Nov 5 15:27:04 2003
※ 引述《barts ( )》之銘言:
: ※ 引述《vicianose ( )》之銘言:
: : 你的意思是說 b1 b2 b3各為 2 1 0 嗎??
: : 但是這樣1*b1*1+2*b2*1+3*b3*1就會不=0耶...^^a
: 所以 2 1 0 是錯的, 2 -1 0 才對
: 1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
但是~你前面不是說~
b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
若a1 a2 a3 = 1 -1 1
b1 b2 b3 = 2 -1 0
就不會=0了耶 ^^||
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.117.204.116
> -------------------------------------------------------------------------- <
作者: unamnesia ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Wed Nov 5 20:16:03 2003
※ 引述《vicianose ( )》之銘言:
: ※ 引述《barts ( )》之銘言:
: : 所以 2 1 0 是錯的, 2 -1 0 才對
: : 1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
: 但是~你前面不是說~
: b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: 若a1 a2 a3 = 1 -1 1
: b1 b2 b3 = 2 -1 0
: 就不會=0了耶 ^^||
建議去找書先從 character table 建構的五個基本定理看起,會比較有通盤的了解
我用很直觀的方式概述
1.character table 必然是 n*n 的形式,列數與行數一定恰好相等
2.E 操作的那一列 (最左方那列) 的平方和一定恰等於上頭操作元素的個數
3.同 class (像2C3 這兩個) 擁有同樣的值
4.5. 大正交定理,直列與橫排都必然彼此正交 (橫排甲*橫排乙*上頭係數 = 0)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.109.112.214
> -------------------------------------------------------------------------- <
作者: barts ( ) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Wed Nov 5 22:26:18 2003
※ 引述《vicianose ( )》之銘言:
: ※ 引述《barts ( )》之銘言:
: : 所以 2 1 0 是錯的, 2 -1 0 才對
: : 1*2*1 + 2*-1*1 + 3*0*1 = 0 就對啦!!
: 但是~你前面不是說~
: b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: 若a1 a2 a3 = 1 -1 1
: b1 b2 b3 = 2 -1 0
: 就不會=0了耶 ^^||
沒有錯, 所以我再看了你的原 post;
你的原post中, A2 寫錯了, A2 應該是 1 1 -1,
因為 A2 和 A1 沒有orthorgonal
兩兩相互是 orthorgaonal的;
請再check C2v 的character table!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.55.137
※ 編輯: barts 來自: 140.112.55.137 (11/05 22:28)
> -------------------------------------------------------------------------- <
作者: satanfh (Satan) 看板: Chemistry
標題: Re: [問題] 群論...
時間: Fri Nov 7 17:09:38 2003
去找個已經懂得同學解釋一次給你聽吧...
這樣最快
^_^
※ 引述《barts ( )》之銘言:
: ※ 引述《vicianose ( )》之銘言:
: : 但是~你前面不是說~
: : b1*a1 + b2*a2 + b3*a3 = 0 (orthorgonal)
: : 若a1 a2 a3 = 1 -1 1
: : b1 b2 b3 = 2 -1 0
: : 就不會=0了耶 ^^||
: 沒有錯, 所以我再看了你的原 post;
: 你的原post中, A2 寫錯了, A2 應該是 1 1 -1,
: 因為 A2 和 A1 沒有orthorgonal
: 兩兩相互是 orthorgaonal的;
: 請再check C2v 的character table!!
--
來看看喔~ ^_^
https://oz.nthu.edu.tw/~d927536/yuxin/index.html
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.109.227.150
... <看更多>