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"D4d 점군"의 두 판 사이의 차이

(새 문서: ==찾아보기== {{점군}} ==개요== ;d4d point group ;d4d 점군 ==지표표== {| class='wikitable' ! !! E !! 2S<sub>8</sub> !! 2C<sub>4</sub> !! 2(S<sub>8</sub>)<sup>3</sup> !!...)
 
 
(사용자 2명의 중간 판 4개는 보이지 않습니다)
3번째 줄: 3번째 줄:


==개요==
==개요==
;d4d point group
;D<sub>4d</sub> point group
;d4d 점군
;D<sub>4d</sub> 점군
*비가환군, 7(10) 기약 표현
*서브그룹: Cs, C<sub>2</sub>, C<sub>4</sub>, D<sub>2</sub>, D<sub>4</sub>, C<sub>2v</sub>, C<sub>4v</sub>, S<sub>8</sub>


==지표표==
==지표표==
{| class='wikitable'
{| class='wikitable'
!  !! E !! 2S<sub>8</sub> !! 2C<sub>4</sub> !! 2(S<sub>8</sub>)<sup>3</sup> !! C<sub>2</sub> !! 4C'<sub>2</sub> !! 4σ<sub>d</sub> !! 선형, 회전 !! 2차
!  !! E !! 2S<sub>8</sub> !! 2C<sub>4</sub> !! 2(S<sub>8</sub>)<sup>3</sup> !! C<sub>2</sub> !! 4C'<sub>2</sub> !! 4σ<sub>d</sub> !! 선형, 회전 !! 2차
|-
|- align='center'
! A<sub>1</sub>  
! A<sub>1</sub>  
| 1 || 1 || 1 || 1 || 1 || 1 || 1 ||  || x<sup>2</sup>+y<sup>2</sup>, z<sup>2</sup>
| 1 || 1 || 1 || 1 || 1 || 1 || 1 ||  || x<sup>2</sup>+y<sup>2</sup>, z<sup>2</sup>
|-
|- align='center'
! A<sub>2</sub>  
! A<sub>2</sub>  
| 1 || 1 || 1 || 1 || 1 || -1 || -1 || R<sub>z</sub> ||  
| 1 || 1 || 1 || 1 || 1 || -1 || -1 || R<sub>z</sub> ||  
|-
|- align='center'
! B<sub>1</sub>  
! B<sub>1</sub>  
| 1 || -1 || 1 || -1 || 1 || 1 || -1 ||  ||  
| 1 || -1 || 1 || -1 || 1 || 1 || -1 ||  ||  
|-
|- align='center'
! B<sub>2</sub>  
! B<sub>2</sub>  
| 1 || -1 || 1 || -1 || 1 || -1 || 1 || z ||  
| 1 || -1 || 1 || -1 || 1 || -1 || 1 || z ||  
|-
|- align='center'
! E<sub>1</sub>  
! E<sub>1</sub>  
| 2 || (2)<sup>1/2</sup> || 0 || -(2)<sup>1/2</sup> || -2 || 0 || 0 || (x, y) ||  
| 2 || (2)<sup>1/2</sup> || 0 || -(2)<sup>1/2</sup> || -2 || 0 || 0 || (x, y) ||  
|-
|- align='center'
! E<sub>2</sub>  
! E<sub>2</sub>  
| 2 || 0 || -2 || 0 || 2 || 0 || 0 ||  || (x<sup>2</sup>-y<sup>2</sup>, xy)
| 2 || 0 || -2 || 0 || 2 || 0 || 0 ||  || (x<sup>2</sup>-y<sup>2</sup>, xy)
|-
|- align='center'
! E<sub>3</sub>
! E<sub>3</sub>
| 2 || -(2)<sup>1/2</sup> || 0 || (2)<sup>1/2</sup> || -2 || 0 || 0 || (R<sub>x</sub>, R<sub>y</sub>) || (xz, yz)
| 2 || -(2)<sup>1/2</sup> || 0 || (2)<sup>1/2</sup> || -2 || 0 || 0 || (R<sub>x</sub>, R<sub>y</sub>) || (xz, yz)
35번째 줄: 37번째 줄:
{| class='wikitable'
{| class='wikitable'
!  !! A<sub>1</sub> !! A<sub>2</sub> !! B<sub>1</sub> !! B<sub>2</sub> !! E<sub>1</sub> !! E<sub>2</sub> !! E<sub>3</sub>
!  !! A<sub>1</sub> !! A<sub>2</sub> !! B<sub>1</sub> !! B<sub>2</sub> !! E<sub>1</sub> !! E<sub>2</sub> !! E<sub>3</sub>
|-
|- align='center'
! A<sub>1</sub>  
! A<sub>1</sub>  
| A<sub>1</sub> || A<sub>2</sub> || B<sub>1</sub> || B<sub>2</sub> || E<sub>1</sub> || E<sub>2</sub> || E<sub>3</sub>
| A<sub>1</sub> || A<sub>2</sub> || B<sub>1</sub> || B<sub>2</sub> || E<sub>1</sub> || E<sub>2</sub> || E<sub>3</sub>
|-
|- align='center'
! A<sub>2</sub>  
! A<sub>2</sub>  
| A<sub>2</sub> || A<sub>1</sub> || B<sub>2</sub> || B<sub>1</sub> || E<sub>1</sub> || E<sub>2</sub> || E<sub>3</sub>
| A<sub>2</sub> || A<sub>1</sub> || B<sub>2</sub> || B<sub>1</sub> || E<sub>1</sub> || E<sub>2</sub> || E<sub>3</sub>
|-
|- align='center'
! B<sub>1</sub>  
! B<sub>1</sub>  
| B<sub>1</sub> || B<sub>2</sub> || A<sub>1</sub> || A<sub>2</sub> || E<sub>3</sub> || E<sub>2</sub> || E<sub>1</sub>
| B<sub>1</sub> || B<sub>2</sub> || A<sub>1</sub> || A<sub>2</sub> || E<sub>3</sub> || E<sub>2</sub> || E<sub>1</sub>
|-
|- align='center'
! B<sub>2</sub>  
! B<sub>2</sub>  
| B<sub>2</sub> || B<sub>1</sub> || A<sub>2</sub> || A<sub>1</sub> || E<sub>3</sub> || E<sub>2</sub> || E<sub>1</sub>
| B<sub>2</sub> || B<sub>1</sub> || A<sub>2</sub> || A<sub>1</sub> || E<sub>3</sub> || E<sub>2</sub> || E<sub>1</sub>
|-
|- align='center'
! E<sub>1</sub>  
! E<sub>1</sub>  
| E<sub>1</sub> || E<sub>1</sub> || E<sub>3</sub> || E<sub>3</sub> || A<sub>1</sub>+A<sub>2</sub>+E<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub> || B<sub>1</sub>+B<sub>2</sub>+E<sub>2</sub>
| E<sub>1</sub> || E<sub>1</sub> || E<sub>3</sub> || E<sub>3</sub> || A<sub>1</sub>+A<sub>2</sub>+E<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub> || B<sub>1</sub>+B<sub>2</sub>+E<sub>2</sub>
|-
|- align='center'
! E<sub>2</sub>  
! E<sub>2</sub>  
| E<sub>2</sub> || E<sub>2</sub> || E<sub>2</sub> || E<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub> || A<sub>1</sub>+A<sub>2</sub>+B<sub>1</sub>+B<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub>
| E<sub>2</sub> || E<sub>2</sub> || E<sub>2</sub> || E<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub> || A<sub>1</sub>+A<sub>2</sub>+B<sub>1</sub>+B<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub>
|-
|- align='center'
! E<sub>3</sub>  
! E<sub>3</sub>  
| E<sub>3</sub> || E<sub>3</sub> || E<sub>1</sub> || E<sub>1</sub> || B<sub>1</sub>+B<sub>2</sub>+E<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub> || A<sub>1</sub>+A<sub>2</sub>+E<sub>2</sub>
| E<sub>3</sub> || E<sub>3</sub> || E<sub>1</sub> || E<sub>1</sub> || B<sub>1</sub>+B<sub>2</sub>+E<sub>2</sub> || E<sub>1</sub>+E<sub>3</sub> || A<sub>1</sub>+A<sub>2</sub>+E<sub>2</sub>
|}
|}
==참고==
*http://www.webqc.org/symmetrypointgroup-d4d.html


[[분류: 점군]]
[[분류: 점군]]

2019년 10월 2일 (수) 14:01 기준 최신판

1 찾아보기[ | ]

접기
대칭 점군

2 개요[ | ]

D4d point group
D4d 점군
  • 비가환군, 7(10) 기약 표현
  • 서브그룹: Cs, C2, C4, D2, D4, C2v, C4v, S8

3 지표표[ | ]

E 2S8 2C4 2(S8)3 C2 4C'2 4σd 선형, 회전 2차
A1 1 1 1 1 1 1 1 x2+y2, z2
A2 1 1 1 1 1 -1 -1 Rz
B1 1 -1 1 -1 1 1 -1
B2 1 -1 1 -1 1 -1 1 z
E1 2 (2)1/2 0 -(2)1/2 -2 0 0 (x, y)
E2 2 0 -2 0 2 0 0 (x2-y2, xy)
E3 2 -(2)1/2 0 (2)1/2 -2 0 0 (Rx, Ry) (xz, yz)

4 곱셈표[ | ]

A1 A2 B1 B2 E1 E2 E3
A1 A1 A2 B1 B2 E1 E2 E3
A2 A2 A1 B2 B1 E1 E2 E3
B1 B1 B2 A1 A2 E3 E2 E1
B2 B2 B1 A2 A1 E3 E2 E1
E1 E1 E1 E3 E3 A1+A2+E2 E1+E3 B1+B2+E2
E2 E2 E2 E2 E2 E1+E3 A1+A2+B1+B2 E1+E3
E3 E3 E3 E1 E1 B1+B2+E2 E1+E3 A1+A2+E2

5 참고[ | ]

원본 주소 "https://zetawiki.com/w/index.php?title=D4d_점군&oldid=535847"
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