Content deleted Content added
m →Formal Definitions: General fixes and Typo fixing, replaced: the where the → where the, typo(s) fixed: where where → where using AWB |
additional clarity |
||
Line 123:
=== Multi-exchange Description ===
Using the addition theorem of tensor operators, the product of a rank n tensor and a rank m tensor can generate a new tensor with rank n+m ~ |n-m|. Therefore, a high rank tensor can be expressed as the inverted circular product of low rank tensors. This convention is useful to interpret and reduce the high rank multipolar exchange terms as a "multi-exchange" process of dipoles (or pseudospins). For example, for the spherical harmonic tensor operators of <math> J=1 </math> case, we have
:<math> Y_{2}^{-2}=2Y_{1}^{-1}Y_{1}^{-1} </math>
:<math> Y_{2}^{-1}=\sqrt{2}(Y_{1}^{-1}Y_{1}^{0}+Y_{1}^{0}Y_{1}^{-1}) </math>
| |||