Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
physics_chemistry:orbitals:k [2016/10/10 09:40] – external edit 127.0.0.1physics_chemistry:orbitals:k [2026/06/20 16:13] (current) – Maurits W. Haverkort
Line 1: Line 1:
 +{{indexmenu_n>3}}
 ====== Kubic Harmonics (K) ====== ====== Kubic Harmonics (K) ======
 ~~NOTOC~~ ~~NOTOC~~
Line 11: Line 12:
  
 ### ###
-The relation between the kubic harmonics and the tesseral harmonics is given by the matrix $T_{Z\,\mathrm{to}\,K}$, whereby the vector $\{Z_{l}^{(m=-l)},K_{l}^{(m=-l+1)},\dots,K_{l}^{(m=l)}\}$ is given as $T_{Z\,\mathrm{to}\,K} \cdot \{Y_{l}^{(m=-l)},Y_{l}^{(m=-l+1)},\dots,Y_{l}^{(m=l)}\}$. Explicit forms of $T_{Z\,\mathrm{to}\,K}$ for $l$ equal or smaller to 6 are:+The relation between the kubic harmonics and the tesseral harmonics is given by the matrix $T_{Z\,\mathrm{to}\,K}$, whereby the vector $\{K_{l}^{(m=-l)},K_{l}^{(m=-l+1)},\dots,K_{l}^{(m=l)}\}$ is given as $T_{Z\,\mathrm{to}\,K} \cdot \{Z_{l}^{(m=-l)},Z_{l}^{(m=-l+1)},\dots,Z_{l}^{(m=l)}\}$. Explicit forms of $T_{Z\,\mathrm{to}\,K}$ for $l$ equal or smaller to 6 are:
 ### ###
  
Line 96: Line 97:
 $$ $$
  
-### 
 The following table shows the kubic harmonics up to $l=6$. We list the explicit function in terms of the directional cosines $x$, $y$ and $z$. The plots show the surface defined by the equation $r={K_l^{(m)}}^* K_l^{(m)}$. The color of the surface is according to the phase with red for positive and cyan for negative. We show a 3D image as well as a projection along the $x$, $y$ and $z$ direction. The following table shows the kubic harmonics up to $l=6$. We list the explicit function in terms of the directional cosines $x$, $y$ and $z$. The plots show the surface defined by the equation $r={K_l^{(m)}}^* K_l^{(m)}$. The color of the surface is according to the phase with red for positive and cyan for negative. We show a 3D image as well as a projection along the $x$, $y$ and $z$ direction.
-### 
  
 ---- ----
Line 516: Line 515:
  
 ====== Different orbital basis sets used ====== ====== Different orbital basis sets used ======
-{{indexmenu>.#1}}+{{indexmenu>.#1|msort}}

You are here: Quanty - a quantum many body script language » Physics, Chemistry and Mathematics » One-particle orbitals » Kubic Harmonics (K)

Print/export