Difference between revisions of "Irr sph ten.m"

From Spinach Documentation Wiki
Jump to: navigation, search
(Created page with "Returns a cell array of single-spin irreducible spherical tensor operators T(k,m). A two-argument call T=irr_sph_ten(mult,k) where 'mult' is the mu...")
 
Line 1: Line 1:
−
Returns a cell array of single-spin irreducible spherical tensor operators T(k,m). A two-argument call
+
{{DISPLAYTITLE:irr_sph_ten.m}}
 +
Single-spin irreducible spherical tensor operators T(k,m). The resulting spherical tensors are normalized in such a way as to obey the following commutation relation:
  
−
                          T=irr_sph_ten(mult,k)
+
    [Lz,T_km]=m*T_km
  
−
where 'mult' is the multiplicity of the spin in question and 'k' is the
+
==Syntax==
−
irreducible spherical tensor rank required, returns a cell array of tensors of that rank in the order of decreasing projection. A single argument call
 
  
−
                          T=irr_sph_ten(mult)
+
    T=irr_sph_ten(mult,k)
  
−
produces tensors of all ranks and concatenates them into a cell array in
+
==Arguments==
−
the order of ascending rank.
 
  
−
The resulting spherical tensors are normalized in such a way as to obey
+
    mult - multiplicity of the spin in question
−
the following commutation relation:
+
 +
        k - irreducible spherical tensor rank (optional)
  
−
                            [Lz,T_lm]=m*T_lm
+
==Outputs==
  
−
Note: operator normalization in spin dynamics is an old and thorny question. Many different conventions exist, but the only way to make the resulting formalism independent of the total spin quantum number is to impose identical commutation relations rather than equal matrix norms.
+
        T - a two-argument call returns a cell array of
 +
            tensors of rank k in the order of decreasing
 +
            projection. A single argument call produces
 +
            tensors of all ranks and puts them into a
 +
            cell array in the order of increasing rank.
 +
 
 +
==Notes==
 +
Operator normalization in spin dynamics is a thorny question. The only way to make the resulting formalism independent of the total spin quantum number is to impose identical commutation relations rather than equal matrix norms.
 +
 
 +
==See also==
 +
[[pauli.m]], [[ist_product_table.m]], [[stevens.m]], [[stev2sph.m]], [[p_superop.m]]
 +
 
 +
 
 +
''Version 2.2, authors: [[Ilya Kuprov]], [[Hannah Hogben]]''

Revision as of 16:42, 29 August 2018

Single-spin irreducible spherical tensor operators T(k,m). The resulting spherical tensors are normalized in such a way as to obey the following commutation relation: 

    [Lz,T_km]=m*T_km

Syntax

    T=irr_sph_ten(mult,k)

Arguments

    mult - multiplicity of the spin in question

       k - irreducible spherical tensor rank (optional)

Outputs

       T - a two-argument call returns a cell array of 
           tensors of rank k in the order of decreasing
           projection. A single argument call produces
           tensors of all ranks and puts them into a 
           cell array in the order of increasing rank.

Notes

Operator normalization in spin dynamics is a thorny question. The only way to make the resulting formalism independent of the total spin quantum number is to impose identical commutation relations rather than equal matrix norms.

See also

pauli.m, ist_product_table.m, stevens.m, stev2sph.m, p_superop.m


Version 2.2, authors: Ilya Kuprov, Hannah Hogben

Retrieved from "https://spindynamics.org/wiki/index.php?title=Irr_sph_ten.m&oldid=3427"