
td character table 在 コバにゃんチャンネル Youtube 的最佳解答

Search
... <看更多>
... <看更多>
#1. Character table for point group Td
Td, E, 8C3, 3C2, 6S4, 6 d. linear functions, rotations. quadratic functions. cubic functions. A1, +1, +1, +1, +1, +1, -, x 2 +y 2 +z 2, xyz.
#2. Character table for the T d point group - Gernot Katzer
Character table for the symmetry point group Td as used in quantum chemistry and spectroscopy, with product and correlation tables and an online form ...
#4. Point Group Symmetry Character Tables - td
Character table for Td point group ; A · 1, 1 ; A · 1, 1 ; E, 2, -1 ; T · 3, 0 ...
#5. 1.5: Character Tables - Chemistry LibreTexts
2022年1月12日 — A character table is a 2 dimensional chart associated with a point group that contains the irreducible representations of each point group ...
#6. Tables for Group Theory - Oxford - UJI
This provides the essential tables (character tables, direct products, ... T, O, Th, Oh, Td ... character tables and direct product table.
#7. A Point Group Character Tables
Appendix A contains Point Group Character (Tables A.1–A.34) to be used ... Character table for group Td for the group of the wave vector for the.
Simulations · | Point Groups · | Character Tables · | Symmetry Operations · | Spectra · | Examples · What is a point group? What is a character table?
#9. Character table for group Td
4, of s-functions on each of 4 atoms on the corners of a regular tetrahedron. These functions are the basis for a. (reducible) representation of ...
#10. Systematic Reduction of Irreducible Representations
Products gc χi χr Td : Character table for T. Character table for Td. (without last column for vector transformations and direct products).
#11. Representations, Character Tables, and One Application of ...
Transformation Matrices. Each symmetry operation can be represented by a 3×3 matrix that shows how the operation transforms a set of x, y, ...
#12. Cubic: Td - Products - University of Exeter
Td character table · Td correlation table ... by unit cell parameters · Correlation table index · 3D objects · Stereographs · A brief description of tables ...
#13. 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.
#14. Group theory
character table. Only orbitals of the same symmetry can be combined to form bonding or antibonding molecular. PCV - Spectroscopy of atoms and molecules ...
#15. Point Group Td - Quanty
2 2, −1 − 1, 2 2, 0 0 ; 3 3, 0 0, −1 − 1, 1 1 ...
#16. Point Group Td - an overview | ScienceDirect Topics
The Td point group is of order 24 with the operations, shown in Table 6.5, together with the characters of the reducible representations for the σ and π ...
#17. D Tables for Double Groups - UFMG
A character table including the double group representations (see, for example Table D.1 for groups O and Td). 2. A table giving the decomposition of the direct ...
#18. how can I limit the length of characters to be shown in the ...
I want to hide the extra characters in a table td if its lengths is more than 50 characters unless I click on that particular td to appear ...
#19. Character tables - SlideShare
Tetrahedral Td Octahedral Oh Linear: D∞h for A-B-A ( i ) C ∞ ... “Representations” Each symmetry operation transforms a molecule to look the same as before (.
#20. c9na00064j1.pdf - The Royal Society of Chemistry
character table. Assuming a perfectly symmetric tetrahedral AB4 molecule (see Figure S2a), the system belongs to the point group Td. The corresponding ...
#21. Matrices and characteristic polynomials for double ... - arXiv
tained in Pauli gauge; the double group Td has been studied in both gauges: while matrices of the irreps and the character tables are ...
#22. List of character tables for chemically important 3D point groups
This lists the character tables for the more common molecular point groups used in the study of molecular symmetry. These tables are based on the ...
#23. 1 trace in the character table of Td for C3 rotation? - Chemistry ...
I think I know now. Choose rotation axis that makes equal angles with the x-, y-, and z-axes so that the C3 rotation essentially permutes the axes.
#24. A Point Group Character Tables
Appendix A contains Point Group Character (Tables A.1–A.34) to be used ... Table A.32. Character table for group Td (cubic)a. Td (43m).
#25. Methane Td Symmetry CH4 - ChemTube3D
Methane has tetrahedral symmetry. All the symmetry elements are displayed interactively, including rotation axes and mirror planes.
#26. L1_Tutorial_Problems.pdf - Hunt Research Group
o The character table for the Td point group is shown to the left, Figure 10, and it tells us the key symmetry operations in this group.
#27. Computational determination of character table and symmetry ...
PM3 program for C24 and C28 fullerenes, Oh and Td symmetry were ... Keywords: Character table, fullerene, symmetry, GAP, hyperchem.
#28. - - OAK RIDGE NATION - OSTI.GOV
4 THE CHARACTER TABLES OF THE POINT GROUPS. 8. 5 . GROUP THEORY AND MOLECULAR ... of them are likely to be found in free molecules - Td, which has the.
#29. Applications of molecular symmetry and group theory - e-PG ...
The character table for Td point group together with 3N vectors on each atom is shown in case is give in table .2. Table .2 Γ3N and character table of Td ...
#30. Lecture Notes in Physics - ResearchGate
The character tables for each of the 32 crystallographic point groups discussed in ... Table 2.30 Character table for point group Td. Td.
#31. GeH4 has Td symmetry. Using the character table given - Chegg
Transcribed image text: GeH4 has Td symmetry. Using the character table given below determine; T E Ay 1 Az 1 E 2 T 3 Tz 3 8C, 3C, 60, 6S, 1 1 1 1 (x2 + y2 + ...
#32. Point-Group Theory Tables - Theoretical Chemistry
Obtention of the character table for the double group ... Td. Like T, but the three C2 are each in the subgroup of an S4 axis.
#33. Applications of Group Theory to the Physics of Solids
3.8 Setting up Character Tables . ... 7.4 Characters for the Direct Product of Groups and Repre- sentations . ... Table 3.34: Character Table for Group Td.
#34. A Point Group Character Tables - UCSD Physics
Appendix A contains Point Group Character (Tables A.1–A.34) to be used ... Table A.32. Character table for group Td (cubic)a. Td (43m).
#35. Chemistry 112 – Midterm Examination - Agapie Group
Periodic and character tables are provided at the end of the exam. ... Construct an MO diagram for a generic compound ML4 of Td symmetry.
#36. a) b) c) d) e) f) g) k) h) l)
Character table : Γx,y has the same characters as the E representation, which is 2-dimensional. ... Compare to characters for Td point group. Td.
#37. 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. ... A12.3.2 Rotational Subgroup of Td, T.
#38. test_3(inorg_s_14) 09.pages
The character table for the Td point group is included below. The energy for the H atoms' 1s orbitals is –13.61 eV. The energies for the C 2s and 2p.
#39. Polyatomic Molecular Orbital Theory - La Salle University
from corresponding character tables by their inspection holding in mind the ... Molecular Orbital Theory – Td character table. Td. E 8C3 3C2 6S4 6sd.
#40. User:Amtoffee/sandbox - Wikibooks, open books for an open ...
1 Td Character Table · 2 Reducible Representation · 3 SALCs and MO diagram · 4 References ...
#41. Character Tables - Point Groups C2v and Td | Course Hero
View Notes - Character Tables - C2v and Td from CHEM 724 at Tulane University. Character Tables - Point Groups C2v and Td.
#42. Applications of Group Theory to the Vibrations of Methane ...
LIST OF TABLES. Character table of the Td symmetry group. Character table of the I'. 15 x. 15 representa. tion. Character table of the rotational and.
#43. sv - CodeNext IT
Γσ = A1g + Eg + T1u Reading off the character table, we see that the group ... IR_D3h QuikIR_D3h IR_C3v IR_C2v MOT_Oh MOTD3h RepMatrix OhReps Td Oh Doh D4h ...
#44. [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 ... 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, ...
#45. Point Group Assignments and Character Tables
axes (bisecting pairs of bonds). 3 S4 axes (coincident with C2. 's). 6 σd. 's (each containing Si and 2. Cl's). Point group: Td. Regular octahedron.
#46. Applications: Hybridization
determine the characters of the representation Γσ. * Don't need to determine Γ(T) since we only need χσ ... and Td character table. C734b Hybridization.
#47. Towards "Inverse" Character Tables? A One-Step Method for ...
Towards "Inverse" Character Tables? A One-Step Method for Decomposing Reducible Representations.
#48. MOLECULAR SYMMETRY
The groups Td and Oh are the groups of the tetrahedron ... Character Table is a table that characterizes the.
#49. CHAPTER 15 ( SOLUTIONS MANUAL ) - Físico-química I - 2
Inspection of the character table of the group Td shows that s spans A1 and that the three p orbitals on the C atom span T2. Hence, the s and p orbitals of ...
#50. Group theory in action: molecular vibrations
unshifted atoms and the contribution to character ... Contributions to character ... 3. μ : character table, x→B1, y→B2, z→A1.
#51. Applications of Group Theory to the Physics of Solids
3.8 Setting up Character Tables . ... 15.4 Character Tables for Groups of the Wave Vector . . . . . 438 ... Table 3.34: Character Table for Group Td.
#52. Td Molecular Orbitals - Alchetron, The Free Social Encyclopedia
In order to obtain the molecular orbitals of a Td molecule, a character table is used to find reducible representations, ...
#53. Group Theory - Genesis Tutorials
Td. 12. On. 24. Matrix Representation of Symmetry operations- ... A character table is a way which can be utilized for application of group theory for the ...
#54. <td>:表格数据单元格元素 - HTML(超文本标记语言) - MDN ...
The content in the cell element is aligned to a character. Typical values include a period (.) to align numbers or monetary values. If align is ...
#55. Character Tables of the General Linear Group and Some of its ...
We describe and list the full character table of GL(3,q). ... polynomial of g is f(t)=(td + ad−1td−1 + ··· + 1)s for some s and hence ∂f = d and d|n.
#56. Character Tables for Point Groups - SlideServe
The point group is Td so we must use the appropriate character table to find the reducible representation of the sigma bonding, first, then ...
#57. Day 1: Discrete Groups G1: smaller groups G2: larger groups
“Character table”. e a1 ... S3 multiplication table can be generated by a and ... Td, O. S4 rder. Isometry group. Abstract group.
#58. Character Tables for the Crystal Point Groups
Their character tables may ... On the right side of each character table are listed, in the row of the irreducible ... 3m (Td). E 3 [8]. 2z [3] md [6] 4.
#59. 1 EXPERIMENT 5 MOLECULAR SYMMETRY, POINT ...
MOLECULAR SYMMETRY, POINT GROUPS AND CHARACTER TABLES ... Note that molecules from the point groups Td, Oh, and Ih will not have dipoles.
#60. TABLES OF FINITE GROUPS by Gabriel Allen Lewis ...
Page 23, Character Table for Group D2: The fourth column should be labeled R3 in-. 2 stead of R4. Page 27, Group Table for Group Td or 0 : The row labeled ...
#61. The character table for the corepresentations of magnetic groups
The table possesses row and column orthogonality properties similar to the character table for linear groups. PACS numbers: 02.20. + b, 11.30. - j. 1.
#62. Molecular Symmetry - FIU Faculty Websites
and in particular to the tetrahedral groups T, Td and Th or to the ... upon the character table of the group – a table that characterizes the different ...
#63. Character Tables
6, I. Use the worksheet tabs at the bottom of the page to select character tables listed in alphabetical order. ... 4, Td, E, 8C3, 3C2, 6S4, 6sd.
#64. Housecroft Inorganic Chemistry 3e - ID:5c18780a9157c
XY4 molecules with Td or D4h symmetry An XY4 molecule with Td symmetry has nine normal modes of vibration (Figure 4.16). In the Td character table (see ...
#65. GROUP THEORY AND ITS APPLICATIONS
4.12 Character Table and Construction of Character. Table for C2v and C3v ... Point group Td : Regular tetrahedra molecules have Td point group.
#66. Molecular Symmetry - Vibrations + Reducible Representations
It is a tetrahedral molecule, therefore we use the Td character table. [1] We need to consider the symmetry operations from the Td table, and their effects ...
#67. 4 Molecular Symmetry - NET
character table of the C2h point group is shown below. ... This molecule has Td symmetry and two types of carbon atoms. There are four methine carbons (each ...
#68. Character Table Hell | Physics Forums
Character Table Hell! ... For example in the C2v character table why does z go with A1, Rx, go with A2, ... YES: Groups Ih, Oh, Td
#69. What is TD point group? - Rampfesthudson.com
Molecules in the Td group, such as methane (CH4) have four C3 rotational axes. The character table for the Td point group is shown below: ...
#70. Chemistry 6330 Problem Set 4 Answers
Problem Set 4 Answers. (1) (a) BF4. - tetrahedral (Td). Td ... By inspection of the character table, the 2T2 modes are IR active and A1, E, and 2T2.
#71. Point Group Assignments and Character Tables - StudyLib
Point Group Assignments and Character Tables Inorganic Chemistry Chapter 1: ... 6 σd's (each containing Si and 2 Cl's) Point group: Td Regular octahedron F ...
#72. Point Group Tables of T d (-43m) - Bilbao Crystallographic ...
Character Table of the group Td(-43m)*. Td(-43m), #, 1, 3, 2100, -4, m110, functions. Mult. -, 1, 8, 3, 6, 6, ·. A1, Γ1, 1, 1, 1, 1, 1, x 2 +y 2 +z 2.
#73. 341_02a.pdf
Character Tables (15.4). Translational, Rotational and Vibrational Character. Introduction: Matrix Representation of Group Theory ... Point groups: Td.
#74. Appendix E-Symmetry.pdf
character table ) of all six symmetry operations are 1 for the A1 irreducible representation. The 2px and 2py orbitals on the nitrogen atom transform as the ...
#75. SOLVED:H2O (C2v point group); NH3 (C3v point ... - Numerade
... CD4 (Td point group); C2H4 (D2h point group) (a) Estimate the number of vibrational modes using the appropriate formula (b) Use the character table to ...
#76. Symmetry Groups - nmsu.edu is a Web Hosting
D3h. On this page you can see the character tables of most of the groups we use. I will try to update the list as soon as I can. You choose a group from the ...
#77. Visit Symmetry.jacobs-university.de - Character tables for ...
Symmetry.jacobs-university.de: Character tables for chemically ... Character table for point group Td Character table for point group T d.
#78. CEM311_Objectives Midterm2 - MSU chemistry
inversion (D∞h); 3) Ideal tetrahedral (Td); 4) Ideal octahedral (Oh); 5) Ideal ... Each point group has its own character table; the first row of a ...
#79. QUESTION BANK CHP -4102 Section I
5) The character table for C2v point group is given below. In cis butadiene molecule the vibrational modes ... c) Td d) C2v. 7) The point group of NOCl is-.
#80. Group Theory Formula Sheet
Componenets of character table. Page 12. Gibbs Free energyhange. Character table of C2v point gp. Character table of C3v ... Character table of Td point ...
#81. Group Theory - Mathematical Physics
2.10 Properties of the Character Table . ... T D = U−1TUU−1MU. = U−1TMU ... The character table is a square matrix with dimension equal to the number.
#82. Group Theory Mini-Exam
Td : Plane contains only v others are reflected into each other. x=1 ... Please use the C3v character table and the irreducible representations from your.
#83. Methane Symmetry Operations - Representation Matrices | NIST
... Methane Symmetry Operations - Td Symmetry Species Expand or Collapse ... Their traces occur as characters in the last row of Table 1.
#84. Resource section 4 Character tables
The character tables that follow are for the most common point groups encountered in inorganic chemistry. Each one is labelled with the symbol adopted in ...
#85. Polyatomic Molecular Orbital Theory - Studylib
H B H y H x Molecular Orbital Theory – D3h Character Table D3h E 2C3 3C2 σh ... Orbital Theory – Td character table Part of the Td Character Table Td E 8C3 ...
#86. HTML Tables - W3Schools
HTML tables allow web developers to arrange data into rows and columns. ... Each table cell is defined by a <td> and a </td> tag. td stands for table data.
#87. Molecular Symmetry - The Chemistry Guru
A character table represents all the symmetry elements correspond to each point group. ... Character table Td point group, methane (CH4).
#88. a) By using the character table of Td show that T2 ? T2 T1 ? T2
a) By using the character table of Td show that T2 ⊗ T2 T1 ⊕ T2 ⊕ E ⊕ A1. b) Verify that the symmetrized linear combinations of the ...
#89. Symmetry
3049) In the Td point group, a clockwise S4 operation using the axis shown ... 3055) From the character table below, how many sets of d orbitals are there ...
#90. Table 1 from Non-Hermitian oscillators with Td symmetry
Table 1: Character table for Td point group - "Non-Hermitian oscillators with Td symmetry"
#91. Table labels in HTML - 前端知识
table,td,tr Three basic form labels. table The properties of are as follows :. border. Used to display the outline of the table in the page ...
#92. Random Character Added to Field Name Upon Publish - Esri ...
Since upgrading to Enterprise 9.1, a weird thing has been occurring when publishing out map services with layers joined to a view table.
#93. Times Tables Rock Stars
Each week concentrates on a different times table, with a recommended consolidation week for rehearsing the tables that have recently been practised every ...
#94. Character Tables | CH 431 Inorganic Chemistry - CNS Sites
Once the point group of a molecule is known, we can begin to make use of character tables. Group theoretical considerations and matrix algebra have produced ...
#95. Fundamentals of Semiconductors: Physics and Materials Properties
Character table and basis functions of the Td group {E} {3C2} {6S4} {6Û} ... 1 1 0 {x,y,z} while the two remaining characters for T1 and T2 contain 1 and 1.
#96. Inorganic Chemistry - 第 76 頁 - Google 圖書結果
TABLE 3.6 The Td character table Td E 8C3 3C2 6S4 6σd h=24 A1 1 1 1 1 1 x2+y2+z2 ] A2 1 1 1 −1 −1 E 2 −1 2 0 0 (2z2−x2−y2, x2−y2) T1 3 0 −1 1 ...
#97. Another Eden Update Patch Notes - March 16, 2022
These Encounters each focus on four characters, including the Cyan ... (Chernobog)[/td][td]Cyan Scyther ... (Magna Rex)[/td][/tr][/table]
td 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>