"D2h 점군"의 두 판 사이의 차이

9번째 줄: 9번째 줄:
!  !! E !! C<sub>2</sub> (z) !! C<sub>2</sub> (y) !! C<sub>2</sub> (x) !! i !! σ (xy) !! σ (xz) !! σ (yz) !! 선형, 회전 !! 2차
!  !! E !! C<sub>2</sub> (z) !! C<sub>2</sub> (y) !! C<sub>2</sub> (x) !! i !! σ (xy) !! σ (xz) !! σ (yz) !! 선형, 회전 !! 2차
|-
|-
| A<sub>g</sub> || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||  || x<sup>2</sup>, y<sup>2</sup>, z<sup>2</sup>
! A<sub>g</sub>  
| 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||  || x<sup>2</sup>, y<sup>2</sup>, z<sup>2</sup>
|-
|-
| B<sub>1g</sub> || 1 || 1 || -1 || -1 || 1 || 1 || -1 || -1 || R<sub>z</sub> || xy
! B<sub>1g</sub> |
1 || 1 || -1 || -1 || 1 || 1 || -1 || -1 || R<sub>z</sub> || xy
|-
|-
| B<sub>2g</sub> || 1 || -1 || 1 || -1 || 1 || -1 || 1 || -1 || R<sub>y</sub> || xz
! B<sub>2g</sub>  
| 1 || -1 || 1 || -1 || 1 || -1 || 1 || -1 || R<sub>y</sub> || xz
|-
|-
| B<sub>3g</sub> || 1 || -1 || -1 || 1 || 1 || -1 || -1 || 1 || R<sub>x</sub> || yz
1 B<sub>3g</sub>  
| 1 || -1 || -1 || 1 || 1 || -1 || -1 || 1 || R<sub>x</sub> || yz
|-
|-
| A<sub>u</sub> || 1 || 1 || 1 || 1 || -1 || -1 || -1 || -1 ||  ||  
! A<sub>u</sub>  
| 1 || 1 || 1 || 1 || -1 || -1 || -1 || -1 ||  ||  
|-
|-
| B<sub>1u</sub> || 1 || 1 || -1 || -1 || -1 || -1 || 1 || 1 || z ||  
! B<sub>1u</sub>  
| 1 || 1 || -1 || -1 || -1 || -1 || 1 || 1 || z ||  
|-
|-
| B<sub>2u</sub> || 1 || -1 || 1 || -1 || -1 || 1 || -1 || 1 || y ||  
! B<sub>2u</sub>  
| 1 || -1 || 1 || -1 || -1 || 1 || -1 || 1 || y ||  
|-
|-
| B<sub>3u</sub> || 1 || -1 || -1 || 1 || -1 || 1 || 1 || -1 || x ||  
! B<sub>3u</sub>  
| 1 || -1 || -1 || 1 || -1 || 1 || 1 || -1 || x ||  
|}
|}


30번째 줄: 38번째 줄:
!  !! A<sub>g</sub> !! B<sub>1g</sub> !! B<sub>2g</sub> !! B<sub>3g</sub> !! A<sub>u</sub> !! B<sub>1u</sub> !! B<sub>2u</sub> !! B<sub>3u</sub>
!  !! A<sub>g</sub> !! B<sub>1g</sub> !! B<sub>2g</sub> !! B<sub>3g</sub> !! A<sub>u</sub> !! B<sub>1u</sub> !! B<sub>2u</sub> !! B<sub>3u</sub>
|-
|-
| A<sub>g</sub> || A<sub>g</sub> || B<sub>1g</sub> || B<sub>2g</sub> || B<sub>3g</sub> || A<sub>u</sub> || B<sub>1u</sub> || B<sub>2u</sub> || B<sub>3u</sub>
! A<sub>g</sub>  
| A<sub>g</sub> || B<sub>1g</sub> || B<sub>2g</sub> || B<sub>3g</sub> || A<sub>u</sub> || B<sub>1u</sub> || B<sub>2u</sub> || B<sub>3u</sub>
|-
|-
| B<sub>1g</sub> || B<sub>1g</sub> || A<sub>g</sub> || B<sub>3g</sub> || B<sub>2g</sub> || B<sub>1u</sub> || A<sub>u</sub> || B<sub>3u</sub> || B<sub>2u</sub>
! B<sub>1g</sub>  
| B<sub>1g</sub> || A<sub>g</sub> || B<sub>3g</sub> || B<sub>2g</sub> || B<sub>1u</sub> || A<sub>u</sub> || B<sub>3u</sub> || B<sub>2u</sub>
|-
|-
| B<sub>2g</sub> || B<sub>2g</sub> || B<sub>3g</sub> || A<sub>g</sub> || B<sub>1g</sub> || B<sub>2u</sub> || B<sub>3u</sub> || A<sub>u</sub> || B<sub>1u</sub>
! B<sub>2g</sub>  
| B<sub>2g</sub> || B<sub>3g</sub> || A<sub>g</sub> || B<sub>1g</sub> || B<sub>2u</sub> || B<sub>3u</sub> || A<sub>u</sub> || B<sub>1u</sub>
|-
|-
| B<sub>3g</sub> || B<sub>3g</sub> || B<sub>2g</sub> || B<sub>1g</sub> || A<sub>g</sub> || B<sub>3u</sub> || B<sub>2u</sub> || B<sub>1u</sub> || A<sub>u</sub>
! B<sub>3g</sub>  
| B<sub>3g</sub> || B<sub>2g</sub> || B<sub>1g</sub> || A<sub>g</sub> || B<sub>3u</sub> || B<sub>2u</sub> || B<sub>1u</sub> || A<sub>u</sub>
|-
|-
| A<sub>u</sub> || A<sub>u</sub> || B<sub>1u</sub> || B<sub>2u</sub> || B<sub>3u</sub> || A<sub>g</sub> || B<sub>1g</sub> || B<sub>2g</sub> || B<sub>3g</sub>
! A<sub>u</sub>  
| A<sub>u</sub> || B<sub>1u</sub> || B<sub>2u</sub> || B<sub>3u</sub> || A<sub>g</sub> || B<sub>1g</sub> || B<sub>2g</sub> || B<sub>3g</sub>
|-
|-
| B<sub>1u</sub> || B<sub>1u</sub> || A<sub>u</sub> || B<sub>3u</sub> || B<sub>2u</sub> || B<sub>1g</sub> || A<sub>g</sub> || B<sub>3g</sub> || B<sub>2g</sub>
! B<sub>1u</sub>  
| B<sub>1u</sub> || A<sub>u</sub> || B<sub>3u</sub> || B<sub>2u</sub> || B<sub>1g</sub> || A<sub>g</sub> || B<sub>3g</sub> || B<sub>2g</sub>
|-
|-
| B<sub>2u</sub> || B<sub>2u</sub> || B<sub>3u</sub> || A<sub>u</sub> || B<sub>1u</sub> || B<sub>2g</sub> || B<sub>3g</sub> || A<sub>g</sub> || B<sub>1g</sub>
! B<sub>2u</sub>  
| B<sub>2u</sub> || B<sub>3u</sub> || A<sub>u</sub> || B<sub>1u</sub> || B<sub>2g</sub> || B<sub>3g</sub> || A<sub>g</sub> || B<sub>1g</sub>
|-
|-
| B<sub>3u</sub> || B<sub>3u</sub> || B<sub>2u</sub> || B<sub>1u</sub> || A<sub>u</sub> || B<sub>3g</sub> || B<sub>2g</sub> || B<sub>1g</sub> || A<sub>g</sub>
! B<sub>3u</sub>  
| B<sub>3u</sub> || B<sub>2u</sub> || B<sub>1u</sub> || A<sub>u</sub> || B<sub>3g</sub> || B<sub>2g</sub> || B<sub>1g</sub> || A<sub>g</sub>
|}
|}



2015년 9월 13일 (일) 17:59 판

1 개요

d2h point gorup
d2h 점군
  • 아벨리언
  • 서브그룹: Cs, Ci, C2, C2v', C2h

2 캐릭터 테이블

1 B3g
E C2 (z) C2 (y) C2 (x) i σ (xy) σ (xz) σ (yz) 선형, 회전 2차
Ag 1 1 1 1 1 1 1 1 x2, y2, z2
1 || 1 || -1 || -1 || 1 || 1 || -1 || -1 || Rz || xy
B2g 1 -1 1 -1 1 -1 1 -1 Ry xz
1 -1 -1 1 1 -1 -1 1 Rx yz
Au 1 1 1 1 -1 -1 -1 -1
B1u 1 1 -1 -1 -1 -1 1 1 z
B2u 1 -1 1 -1 -1 1 -1 1 y
B3u 1 -1 -1 1 -1 1 1 -1 x

3 곱셈 표

Ag B1g B2g B3g Au B1u B2u B3u
Ag Ag B1g B2g B3g Au B1u B2u B3u
B1g B1g Ag B3g B2g B1u Au B3u B2u
B2g B2g B3g Ag B1g B2u B3u Au B1u
B3g B3g B2g B1g Ag B3u B2u B1u Au
Au Au B1u B2u B3u Ag B1g B2g B3g
B1u B1u Au B3u B2u B1g Ag B3g B2g
B2u B2u B3u Au B1u B2g B3g Ag B1g
B3u B3u B2u B1u Au B3g B2g B1g Ag

4 참고 자료

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