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--- physics_chemistry:point_groups:d3d [2018/03/21 18:36] – created Stefano Agrestini
+++ physics_chemistry:point_groups:d3d [2018/03/23 10:57] (current) – Stefano Agrestini
@@ Line 1: / Line 1: @@
-====== D3d ======
+====== Point Group D3d ======
+===== Character Table =====
 ###
-alligned paragraph text
+|    ^  $ \text{E} \,{\text{(1)}}  $^$  C_3 \,{\text{(2)}}  $^$  C_2 \,{\text{(3)}}  $^$  \text{i} \,{\text{(1)}}  $^$  S_6 \,{\text{(2)}}  $^$  \sigma_d \,{\text{(3)}} $  ^
+^  $A_{1g}$  |   $1$  |   $1$  |   $1$  |   $1$  |   $1$  |   $1$  |
+^  $A_{2g}$  |   $1$  |   $1$  |   $-1$  |   $1$  |   $1$  |   $-1$  |
+^  $E_g$  |   $2$  |   $-1$  |   $0$  |   $2$  |   $-1$  |   $0$  |
+^  $A_{1u}$  |   $1$  |   $1$  |   $1$  |   $-1$  |   $-1$  |   $-1$  |
+^  $A_{2u}$  |   $1$  |   $1$  |   $-1$  |   $-1$  |   $-1$  |   $1$  |
+^  $E_u$  |   $2$  |   $-1$  |   $0$  |   $-2$  |   $1$  |   $0$  |
 ###
-===== Example =====
+===== Product Table =====
 ###
-description text
+|    ^   $A_{1g}$   ^   $A_{2g}$   ^   $E_g$   ^   $A_{1u}$   ^   $A_{2u}$   ^   $E_u$   ^
+^  $A_{1g}$   |  $A_{1g}$   |  $A_{2g}$   |  $E_g$   |  $A_{1u}$   |  $A_{2u}$   |  $E_u$   |
+^  $A_{2g}$   |  $A_{2g}$   |  $A_{1g}$   |  $E_g$   |  $A_{2u}$   |  $A_{1u}$   |  $E_u$   |
+^  $E_g$   |  $E_g$   |  $E_g$   |  $A_{1g}+A_{2g}+E_g$   |  $E_u$   |  $E_u$   |  $A_{1u}+A_{2u}+E_u$   |
+^  $A_{1u}$   |  $A_{1u}$   |  $A_{2u}$   |  $E_u$   |  $A_{1g}$   |  $A_{2g}$   |  $E_g$   |
+^  $A_{2u}$   |  $A_{2u}$   |  $A_{1u}$   |  $E_u$   |  $A_{2g}$   |  $A_{1g}$   |  $E_g$   |
+^  $E_u$   |  $E_u$   |  $E_u$   |  $A_{1u}+A_{2u}+E_u$   |  $E_g$   |  $E_g$   |  $A_{1g}+A_{2g}+E_g$   |
 ###
-==== Input ====
+===== Implemented Settings =====
-<code Quanty Example.Quanty>
--- some example code
-</code>
-==== Result ====
+[[physics_chemistry:point_groups:d3d:orientation_111| D3d_111 ]] [[physics_chemistry:point_groups:d3d:orientation_zx| D3d_Zx ]] [[physics_chemistry:point_groups:d3d:orientation_zx_a| D3d_Zx_A ]] [[physics_chemistry:point_groups:d3d:orientation_zx_b| D3d_Zx_B ]] [[physics_chemistry:point_groups:d3d:orientation_z(x-y)| D3d_Z(x-y) ]] [[physics_chemistry:point_groups:d3d:orientation_z(x-y)_a| D3d_Z(x-y)_A ]] [[physics_chemistry:point_groups:d3d:orientation_z(x-y)_b| D3d_Z(x-y)_B ]] [[physics_chemistry:point_groups:d3d:orientation_zy| D3d_Zy ]] [[physics_chemistry:point_groups:d3d:orientation_zy_a| D3d_Zy_A ]] [[physics_chemistry:point_groups:d3d:orientation_zy_b| D3d_Zy_B ]]
-<WRAP center box 100%>
-text produced as output
-</WRAP>
-===== Table of contents =====
+==== Setting 111 ====
-{{indexmenu>.#2}}
+[[physics_chemistry:point_groups:d3d:orientation_111|Details of the D3d group in with setting 111]]
+{{:physics_chemistry:pointgroup:d3d_111.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{1,1,1\}$  ,  $\{-1,-1,-1\}$  , |
+^  $C_2$  |  $\{1,-1,0\}$  ,  $\{0,1,-1\}$  ,  $\{1,0,-1\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{1,1,1\}$  ,  $\{-1,-1,-1\}$  , |
+^  $\sigma _d$  |  $\{1,-1,0\}$  ,  $\{0,1,-1\}$  ,  $\{1,0,-1\}$  , |
+###
+==== Setting Zx ====
+[[physics_chemistry:point_groups:d3d:orientation_zx|Details of the D3d group in with setting Zx]]
+{{:physics_chemistry:pointgroup:d3d_zx.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{1,0,0\}$  ,  $\left\{1,\sqrt{3},0\right\}$  ,  $\left\{-1,\sqrt{3},0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{1,0,0\}$  ,  $\left\{1,\sqrt{3},0\right\}$  ,  $\left\{-1,\sqrt{3},0\right\}$  , |
+###
+==== Setting Zx_A ====
+[[physics_chemistry:point_groups:d3d:orientation_zx_a|Details of the D3d group in with setting Zx_A]]
+{{:physics_chemistry:pointgroup:d3d_zx_a.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{1,0,0\}$  ,  $\left\{1,\sqrt{3},0\right\}$  ,  $\left\{-1,\sqrt{3},0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{1,0,0\}$  ,  $\left\{1,\sqrt{3},0\right\}$  ,  $\left\{-1,\sqrt{3},0\right\}$  , |
+###
+==== Setting Zx_B ====
+[[physics_chemistry:point_groups:d3d:orientation_zx_b|Details of the D3d group in with setting Zx_B]]
+{{:physics_chemistry:pointgroup:d3d_zx_b.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{1,0,0\}$  ,  $\left\{1,\sqrt{3},0\right\}$  ,  $\left\{-1,\sqrt{3},0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{1,0,0\}$  ,  $\left\{1,\sqrt{3},0\right\}$  ,  $\left\{-1,\sqrt{3},0\right\}$  , |
+###
+==== Setting Z(x-y) ====
+[[physics_chemistry:point_groups:d3d:orientation_z(x-y)|Details of the D3d group in with setting Z(x-y)]]
+{{:physics_chemistry:pointgroup:d3d_z(x-y).png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{1,-1,0\}$  ,  $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$  ,  $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{1,-1,0\}$  ,  $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$  ,  $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$  , |
+###
+==== Setting Z(x-y)_A ====
+[[physics_chemistry:point_groups:d3d:orientation_z(x-y)_a|Details of the D3d group in with setting Z(x-y)_A]]
+{{:physics_chemistry:pointgroup:d3d_z(x-y)_a.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{1,-1,0\}$  ,  $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$  ,  $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{1,-1,0\}$  ,  $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$  ,  $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$  , |
+###
+==== Setting Z(x-y)_B ====
+[[physics_chemistry:point_groups:d3d:orientation_z(x-y)_b|Details of the D3d group in with setting Z(x-y)_B]]
+{{:physics_chemistry:pointgroup:d3d_z(x-y)_b.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{1,-1,0\}$  ,  $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$  ,  $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{1,-1,0\}$  ,  $\left\{1+\sqrt{3},\sqrt{3}-1,0\right\}$  ,  $\left\{1-\sqrt{3},-1-\sqrt{3},0\right\}$  , |
+###
+==== Setting Zy ====
+[[physics_chemistry:point_groups:d3d:orientation_zy|Details of the D3d group in with setting Zy]]
+{{:physics_chemistry:pointgroup:d3d_zy.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{0,1,0\}$  ,  $\left\{\sqrt{3},1,0\right\}$  ,  $\left\{\sqrt{3},-1,0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{0,1,0\}$  ,  $\left\{\sqrt{3},1,0\right\}$  ,  $\left\{\sqrt{3},-1,0\right\}$  , |
+###
+==== Setting Zy_A ====
+[[physics_chemistry:point_groups:d3d:orientation_zy_a|Details of the D3d group in with setting Zy_A]]
+{{:physics_chemistry:pointgroup:d3d_zy_a.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{0,1,0\}$  ,  $\left\{\sqrt{3},1,0\right\}$  ,  $\left\{\sqrt{3},-1,0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{0,1,0\}$  ,  $\left\{\sqrt{3},1,0\right\}$  ,  $\left\{\sqrt{3},-1,0\right\}$  , |
+###
+==== Setting Zy_B ====
+[[physics_chemistry:point_groups:d3d:orientation_zy_b|Details of the D3d group in with setting Zy_B]]
+{{:physics_chemistry:pointgroup:d3d_zy_b.png }}
+###
+^ Operator ^ Orientation ^
+^  $\text{E}$  |  $\{0,0,0\}$  , |
+^  $C_3$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $C_2$  |  $\{0,1,0\}$  ,  $\left\{\sqrt{3},1,0\right\}$  ,  $\left\{\sqrt{3},-1,0\right\}$  , |
+^  $\text{i}$  |  $\{0,0,0\}$  , |
+^  $S_6$  |  $\{0,0,1\}$  ,  $\{0,0,-1\}$  , |
+^  $\sigma _d$  |  $\{0,1,0\}$  ,  $\left\{\sqrt{3},1,0\right\}$  ,  $\left\{\sqrt{3},-1,0\right\}$  , |
+###
+===== Table of several point groups =====
+###
+[[physics_chemistry:point_groups|Return to Main page on Point Groups]]
+###
+###
+^Nonaxial groups      | [[physics_chemistry:point_groups:c1|C]]<sub>[[physics_chemistry:point_groups:c1|1]]</sub> | [[physics_chemistry:point_groups:cs|C]]<sub>[[physics_chemistry:point_groups:cs|s]]</sub> | [[physics_chemistry:point_groups:ci|C]]<sub>[[physics_chemistry:point_groups:ci|i]]</sub> | | | | |
+^C<sub>n</sub> groups | [[physics_chemistry:point_groups:c2|C]]<sub>[[physics_chemistry:point_groups:c2|2]]</sub> | [[physics_chemistry:point_groups:c3|C]]<sub>[[physics_chemistry:point_groups:c3|3]]</sub> | [[physics_chemistry:point_groups:c4|C]]<sub>[[physics_chemistry:point_groups:c4|4]]</sub> | [[physics_chemistry:point_groups:c5|C]]<sub>[[physics_chemistry:point_groups:c5|5]]</sub> | [[physics_chemistry:point_groups:c6|C]]<sub>[[physics_chemistry:point_groups:c6|6]]</sub> | [[physics_chemistry:point_groups:c7|C]]<sub>[[physics_chemistry:point_groups:c7|7]]</sub> | [[physics_chemistry:point_groups:c8|C]]<sub>[[physics_chemistry:point_groups:c8|8]]</sub> |
+^D<sub>n</sub> groups | [[physics_chemistry:point_groups:d2|D]]<sub>[[physics_chemistry:point_groups:d2|2]]</sub> | [[physics_chemistry:point_groups:d3|D]]<sub>[[physics_chemistry:point_groups:d3|3]]</sub> | [[physics_chemistry:point_groups:d4|D]]<sub>[[physics_chemistry:point_groups:d4|4]]</sub> | [[physics_chemistry:point_groups:d5|D]]<sub>[[physics_chemistry:point_groups:d5|5]]</sub> | [[physics_chemistry:point_groups:d6|D]]<sub>[[physics_chemistry:point_groups:d6|6]]</sub> | [[physics_chemistry:point_groups:d7|D]]<sub>[[physics_chemistry:point_groups:d7|7]]</sub> | [[physics_chemistry:point_groups:d8|D]]<sub>[[physics_chemistry:point_groups:d8|8]]</sub> |
+^C<sub>nv</sub> groups | [[physics_chemistry:point_groups:c2v|C]]<sub>[[physics_chemistry:point_groups:c2v|2v]]</sub> | [[physics_chemistry:point_groups:c3v|C]]<sub>[[physics_chemistry:point_groups:c3v|3v]]</sub> | [[physics_chemistry:point_groups:c4v|C]]<sub>[[physics_chemistry:point_groups:c4v|4v]]</sub> | [[physics_chemistry:point_groups:c5v|C]]<sub>[[physics_chemistry:point_groups:c5v|5v]]</sub> | [[physics_chemistry:point_groups:c6v|C]]<sub>[[physics_chemistry:point_groups:c6v|6v]]</sub> | [[physics_chemistry:point_groups:c7v|C]]<sub>[[physics_chemistry:point_groups:c7v|7v]]</sub> | [[physics_chemistry:point_groups:c8v|C]]<sub>[[physics_chemistry:point_groups:c8v|8v]]</sub> |
+^C<sub>nh</sub> groups | [[physics_chemistry:point_groups:c2h|C]]<sub>[[physics_chemistry:point_groups:c2h|2h]]</sub> | [[physics_chemistry:point_groups:c3h|C]]<sub>[[physics_chemistry:point_groups:c3h|3h]]</sub> | [[physics_chemistry:point_groups:c4h|C]]<sub>[[physics_chemistry:point_groups:c4h|4h]]</sub> | [[physics_chemistry:point_groups:c5h|C]]<sub>[[physics_chemistry:point_groups:c5h|5h]]</sub> | [[physics_chemistry:point_groups:c6h|C]]<sub>[[physics_chemistry:point_groups:c6h|6h]]</sub> | | |
+^D<sub>nh</sub> groups | [[physics_chemistry:point_groups:d2h|D]]<sub>[[physics_chemistry:point_groups:d2h|2h]]</sub> | [[physics_chemistry:point_groups:d3h|D]]<sub>[[physics_chemistry:point_groups:d3h|3h]]</sub> | [[physics_chemistry:point_groups:d4h|D]]<sub>[[physics_chemistry:point_groups:d4h|4h]]</sub> | [[physics_chemistry:point_groups:d5h|D]]<sub>[[physics_chemistry:point_groups:d5h|5h]]</sub> | [[physics_chemistry:point_groups:d6h|D]]<sub>[[physics_chemistry:point_groups:d6h|6h]]</sub> | [[physics_chemistry:point_groups:d7h|D]]<sub>[[physics_chemistry:point_groups:d7h|7h]]</sub> | [[physics_chemistry:point_groups:d8h|D]]<sub>[[physics_chemistry:point_groups:d8h|8h]]</sub> |
+^D<sub>nd</sub> groups | [[physics_chemistry:point_groups:d2d|D]]<sub>[[physics_chemistry:point_groups:d2d|2d]]</sub> | [[physics_chemistry:point_groups:d3d|D]]<sub>[[physics_chemistry:point_groups:d3d|3d]]</sub> | [[physics_chemistry:point_groups:d4d|D]]<sub>[[physics_chemistry:point_groups:d4d|4d]]</sub> | [[physics_chemistry:point_groups:d5d|D]]<sub>[[physics_chemistry:point_groups:d5d|5d]]</sub> | [[physics_chemistry:point_groups:d6d|D]]<sub>[[physics_chemistry:point_groups:d6d|6d]]</sub> | [[physics_chemistry:point_groups:d7d|D]]<sub>[[physics_chemistry:point_groups:d7d|7d]]</sub> | [[physics_chemistry:point_groups:d8d|D]]<sub>[[physics_chemistry:point_groups:d8d|8d]]</sub> |
+^S<sub>n</sub> groups | [[physics_chemistry:point_groups:S2|S]]<sub>[[physics_chemistry:point_groups:S2|2]]</sub> | [[physics_chemistry:point_groups:S4|S]]<sub>[[physics_chemistry:point_groups:S4|4]]</sub> | [[physics_chemistry:point_groups:S6|S]]<sub>[[physics_chemistry:point_groups:S6|6]]</sub> | [[physics_chemistry:point_groups:S8|S]]<sub>[[physics_chemistry:point_groups:S8|8]]</sub> | [[physics_chemistry:point_groups:S10|S]]<sub>[[physics_chemistry:point_groups:S10|10]]</sub> | [[physics_chemistry:point_groups:S12|S]]<sub>[[physics_chemistry:point_groups:S12|12]]</sub> |  |
+^Cubic groups | [[physics_chemistry:point_groups:T|T]] | [[physics_chemistry:point_groups:Th|T]]<sub>[[physics_chemistry:point_groups:Th|h]]</sub> | [[physics_chemistry:point_groups:Td|T]]<sub>[[physics_chemistry:point_groups:Td|d]]</sub> | [[physics_chemistry:point_groups:O|O]] | [[physics_chemistry:point_groups:Oh|O]]<sub>[[physics_chemistry:point_groups:Oh|h]]</sub> | [[physics_chemistry:point_groups:I|I]] | [[physics_chemistry:point_groups:Ih|I]]<sub>[[physics_chemistry:point_groups:Ih|h]]</sub> |
+^Linear groups      | [[physics_chemistry:point_groups:cinfv|C]]<sub>[[physics_chemistry:point_groups:cinfv| $\infty$ v]]</sub> | [[physics_chemistry:point_groups:cinfv|D]]<sub>[[physics_chemistry:point_groups:dinfh| $\infty$ h]]</sub> | | | | | |
+###

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