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oop_ciss_initialRotationDensityMatrix.nb 91.21 KiB
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\[Sigma]Tm transforms into :
1/2 Sin[\[Theta]]^2 \[Sigma]T0 + Sin[\[Theta]/2]^4 \[Sigma]Tp + \
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+ 1/2 Sin[\[Theta]] {Cos[\[Phi]] (Sya + Syb) - Sin[\[Phi]] (Sxa + \
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- 1/4 Sin[2 \[Theta]] {Cos[\[Phi]] (Syz + Szy) - Sin[\[Phi]] (Sxz \
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- 1/4 Sin[\[Theta]]^2 {Cos[2 \[Phi]] (Sxx - Syy) + Sin[2 \[Phi]] (Sxy \
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\[Sigma]ud transforms into :
1/4 Cos[2\[Theta]] \[Sigma]T0 - 1/4 Cos[\[Theta]]^2 (\[Sigma]Tp + \
\[Sigma]Tm) + 1/4 \[Sigma]S0 + 1/2 Cos[\[Theta]](Sza - Szb)
- 1/2 Sin[\[Theta]] {Cos[\[Phi]] (Sya - Syb) - Sin[\[Phi]] (Sxa \
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+ 1/4 Sin[2\[Theta]] {Cos[\[Phi]] (Syz + Szy) - Sin[\[Phi]] (Sxz + \
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+ 1/4 Sin[\[Theta]]^2 {Cos[2\[Phi]](Sxx - Syy) + Sin[2\[Phi]] \
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where the first line is equal to zInvUd = {- 1/4 \
Sin[\[Theta]]^2(Sxx + Syy) - 1/2 Cos[\[Theta]]^2(Szz) + 1/2 Cos[\[Theta]](Sza \
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therefore one can also write it as:
- 1/2 Cos[\[Theta]]^2 \t\t\tSzz
- 1/2 Sin[\[Theta]]^2 Sin[\[Phi]]^2\t\tSxx
- 1/2 Sin[\[Theta]]^2 Cos[\[Phi]]^2\t\tSyy
+ 1/2 Cos[\[Theta]]\t\t\t\t(Sza - Szb)
- 1/2 Sin[\[Theta]] \tCos[\[Phi]] \t\t(Sya - Syb)
+ 1/2 Sin[\[Theta]] \tSin[\[Phi]] \t\t(Sxa - Sxb)
+ 1/4 Sin[2\[Theta]] Cos[\[Phi]] \t\t(Syz + Szy)
- 1/4 Sin[2\[Phi]] \tSin[\[Phi]] \t\t(Sxz + Szx)
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