Difference between revisions of "GellMann"

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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
|req=[[opt_args]]
 
 
|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=1.00}}
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|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==
<pre>
+
<syntaxhighlight>
 
>> GellMann(1)
 
>> GellMann(1)
  
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   (1,1)        1
 
   (1,1)        1
 
   (2,2)      -1
 
   (2,2)      -1
</pre>
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</syntaxhighlight>
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{{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:

\(g_0 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) \(g_1 = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\) \(g_2 = \begin{bmatrix} 0 & -i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\) \(g_3 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{bmatrix}\) \(g_4 = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{bmatrix}\)
\(g_5 = \begin{bmatrix} 0 & 0 & -i \\ 0 & 0 & 0 \\ i & 0 & 0 \end{bmatrix}\) \(g_6 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}\) \(g_7 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & -i \\ 0 & i & 0 \end{bmatrix}\) \(g_8 = \frac{1}{\sqrt{3}} \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{bmatrix}\)

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)       -1

Source code

Click here to view this function's source code on github.

External links