GellMann: Difference between revisions
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Created page with "{{Function |name=GellMann |desc=Produces a Gell-Mann operator |req=opt_args |rel=GenGellMann<br />GenPauli<br />Pauli |upd=December 18, 2013 |v=1.00}} <tt>'''G..." |
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|name=GellMann | |name=GellMann | ||
|desc=Produces a Gell-Mann operator | |desc=Produces a Gell-Mann operator | ||
|rel=[[GenGellMann]]<br />[[GenPauli]]<br />[[Pauli]] | |rel=[[GenGellMann]]<br />[[GenPauli]]<br />[[Pauli]] | ||
|cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]] | |||
|upd=December 18, 2013 | |upd=December 18, 2013 | ||
|v= | |v=0.50}} | ||
<tt>'''GellMann'''</tt> is a [[List of functions|function]] that produces the 3-by-3 Gell-Mann matrices, as defined here: | <tt>'''GellMann'''</tt> is a [[List of functions|function]] that produces the 3-by-3 Gell-Mann matrices, as defined here: | ||
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==Examples== | ==Examples== | ||
< | <syntaxhighlight> | ||
>> GellMann(1) | >> GellMann(1) | ||
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(1,1) 1 | (1,1) 1 | ||
(2,2) -1 | (2,2) -1 | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=GellMann}} | |||
==External links== | ==External links== | ||
* [http://en.wikipedia.org/wiki/Gell-Mann_matrices Gell-Mann matrices] at Wikipedia | * [http://en.wikipedia.org/wiki/Gell-Mann_matrices Gell-Mann matrices] at Wikipedia | ||
Latest revision as of 15:14, 29 September 2014
| GellMann | |
| Produces a Gell-Mann operator | |
| Other toolboxes required | none |
|---|---|
| Related functions | GenGellMann GenPauli Pauli |
| Function category | Special states, vectors, and operators |
GellMann is a function that produces the 3-by-3 Gell-Mann matrices, as defined here:
<math>g_0 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}</math> <math>g_1 = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}</math> <math>g_2 = \begin{bmatrix} 0 & -i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}</math> <math>g_3 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{bmatrix}</math> <math>g_4 = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{bmatrix}</math> <math>g_5 = \begin{bmatrix} 0 & 0 & -i \\ 0 & 0 & 0 \\ i & 0 & 0 \end{bmatrix}</math> <math>g_6 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}</math> <math>g_7 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & -i \\ 0 & i & 0 \end{bmatrix}</math> <math>g_8 = \frac{1}{\sqrt{3}} \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{bmatrix}</math>
Syntax
- G = GellMann(IND)
- G = GellMann(IND,SP)
Argument descriptions
- IND: An index indicating which Gell-Mann operator you would like to be generated. Should be an integer between 0 and 8, inclusive.
- SP (optional, default 0): A flag (either 1 or 0) indicating that the Gell-Mann operator produced should or should not be sparse.
Examples
>> GellMann(1)
ans =
0 1 0
1 0 0
0 0 0
>> GellMann(3,1) % the matrix produced here will be sparse
ans =
(1,1) 1
(2,2) -1Source code
Click here to view this function's source code on github.
External links
- Gell-Mann matrices at Wikipedia