Revision as of 04:47, 25 August 2015 edit Bgwhite (talk \| contribs) Extended confirmed users 547,151 edits WP:CHECKWIKI error fix #94. Stray ref tag. Do general fixes and cleanup if needed. -, typo(s) fixed: e.g → e.g. (3), a example → an example using AWB (11377) ← Previous edit		Revision as of 21:26, 25 August 2015 edit undo 128.200.93.30 (talk) No edit summary Next edit →
Line 123: === Multi-exchange Description === Using the addition ~~rules~~theorem of tensor operators, athe 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 product of low rank tensors. This convention is useful to interpret 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>

Multipolar exchange interaction: Difference between revisions