Needs@"SpinDynamica`"D
spherical tensor operators
? opT
opT@ j,81,m<D defines a first-rank spherical tensor operator for spin j.
opT@81,m<D defaults to opT@1,81,m<D.
opT@8 j,k<,82,m<D defines a second-rank spherical tensor operator for spins j and k.
opT@2,mD defaults to opT@81,2<,82,m<D
opT@88 j,l j <,8k,lk <..<,8L,M<D generates a Lth rank ISTO by coupling together
the interactions 88 j,l j <,8k,lk <..< where j is a symbol identifying the interaction and l j is its rank.
In cases where there are many possible couplings the form opT@88 j,l j <,8k,lk <..<,8L,M<,nD
must be used where n is an integer identifying the coupling scheme.
opT@8 j,k..<,8L,M<D defaults to opT@88 j,1<,8k,1<..<,8L,M<D.
The option Normalize->True may be set to generate STOs normalized in the current state basis.
single spin-1/2
SetSpinSystem@1D
SetSpinSystem::set : the spin system has been set to ::1,
1
2
>>
1
SetBasis::set : the state basis has been set to ZeemanBasisB::1,
opT@1, 81, 0<D
2
>>, BasisLabels ® AutomaticF.
I1 z
opT@1, 82, 0<D
opT::singlespinranktoohigh : spin system does not support a single-spin irreducible spherical tensor operator of rank 2
0
opT@1, 81, 1<D
-
I+1
2
opT@1, 81, - 1<D
I-1
2
single spin-3/2
2
opT.nb
single spin-3/2
SetSpinSystem@881, 3 • 2<<D
SetSpinSystem::set : the spin system has been set to ::1,
3
2
>>
3
SetBasis::set : the state basis has been set to ZeemanBasisB::1,
2
opT@1, 81, 0<D
>>, BasisLabels ® AutomaticF.
I1 z
opT@1, 82, 0<D
-
I-1 .I+1
2
-
6
I+1 .I-1
2
2
+
3
6
I1 z .I1 z
opT@1, 82, 2<D
1
2
I+1 .I+1
opT@1, 83, 0<D
-
I-1 .I+1 .I1 z
2
-
I-1 .I1 z .I+1
10
2
10
-
I+1 .I-1 .I1 z
2
10
-
I+1 .I1 z .I-1
2
-
I1 z .I-1 .I+1
10
2
10
-
I1 z .I+1 .I-1
2
10
opT@1, 83, 3<D
-
I+1 .I+1 .I+1
2
2
spin-1/2 pairs
SetSpinSystem@2D
SetSpinSystem::set : the spin system has been set to ::1,
1
2
>, :2,
1
2
1
SetBasis::set : the state basis has been set to ZeemanBasisB::1,
opT@1, 81, 0<D
I1 z
2
>>
>, :2,
1
2
>>, BasisLabels ® AutomaticF.
2
+
5
I1 z .I1 z .I1 z
opT.nb
opT@81, 2<, 82, 0<D
-
I-1 .I+2
2
-
6
I+1 .I-2
2
2
+
3
6
I1 z .I2 z
opT@81, 2<, 81, 1<D
1
I+1 .I2 z +
-
2
1
2
I1 z .I+2
opT@81, 2<, 82, 2<D
1
2
I+1 .I+2
3 spins-1/2
SetSpinSystem@3D
SetSpinSystem::set : the spin system has been set to ::1,
1
2
>, :2,
1
2
1
SetBasis::set : the state basis has been set to ZeemanBasisB::1,
2
opT@1, 81, 0<D
I1 z
opT@81, 2<, 82, 0<D
-
I-1 .I+2
2
-
6
I+1 .I-2
2
2
+
3
6
I1 z .I2 z
opT@81, 2<, 81, 1<D
1
I+1 .I2 z +
-
2
1
2
I1 z .I+2
opT@81, 2<, 82, 2<D
1
2
I+1 .I+2
opT@81, 2, 3<, 83, 3<D
-
I+1 .I+2 .I+3
2
2
opT@81, 2, 3<, 83, 2<D
I+1 .I+2 .I3 z
2
3
+
I+1 .I2 z .I+3
2
3
+
I1 z .I+2 .I+3
2
3
>, :3,
>, :2,
1
2
1
2
>>
>, :3,
1
2
>>, BasisLabels ® AutomaticF.
3
4
opT.nb
opT@81, 2, 3<, 82, 2<D
opT::multiple :
There are 2 operators with this specification. A list of all possibilities has been returned. Specify a single operator using
the form opT@interactions,8Lam,M<,indexD where index is an integer.
:
I+1 .I2 z .I+3
2
-
2
I1 z .I+2 .I+3
2
,
I+1 .I+2 .I3 z
2
6
opT@81, 2, 3<, 82, 2<, 1D
I+1 .I2 z .I+3
2
-
2
I1 z .I+2 .I+3
2
2
opT@81, 2, 3<, 82, 2<, 2D
I+1 .I+2 .I3 z
6
-
I+1 .I2 z .I+3
2
6
-
I1 z .I+2 .I+3
2
6
-
I+1 .I2 z .I+3
2
6
-
I1 z .I+2 .I+3
2
6
>