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Examples / Re: Spin 1 quadrupolar powder patterns
« on: January 10, 2013, 12:28:29 PM »
It seems like there is only opT["I",{2,0}]  in your Hamiltonian:

HQ[\[CapitalOmega]_]:=Simplify@ExpToTrig[\[Omega]Q*{-\[Eta]Q/Sqrt[6],0,1,0,-\[Eta]Q/Sqrt[6]}.WignerD[2,{{0}}][\[CapitalOmega]]*opT[I,{2,0}]/Sqrt[6]];

Shouldn't opT["I",{2,0}] be a matrix of {opT["I", {2, -2}], opT["I", {2, -1}], opT["I", {2, 0}], opT["I", {2, 1}], opT["I", {2, 2}]}? This is so that the components of the Wigner matrix will multiply by their respective tensor operators.

1K

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I attempt to simulate the spectrum from my Hamiltonian:

H0t[\[Beta]_] :=  2 \[Pi] 10^3 Sqrt[6]/  4 (3/5 \[Omega]d*(3 Cos[\[Beta]]^2 - 1)*opT[2, {2, 0}]* opT [1, {2, 0}] +  cf ((3 Cos[\[Beta]]^2 - 1)*opT [1, {2, 0}] +  s/Sqrt[6]  (-(3/2) Sin[\[Beta]]^2*opT[1, {2, 2}] -  3/2 Sin[\[Beta]]^2*opT[1, {2, -2}]))) ,
with SetSpinSystem[{{1, 1}, {2, 1}}].

However, it took an exceptionally long time to simulate. So I tried simulating only the part of the Hamiltonian which only involves a single spin 1 particle:

H0t[\[Beta]_] :=  2 \[Pi] 10^3 Sqrt[6]/  4 cf*((3 Cos[\[Beta]]^2 - 1)*opT [1, {2, 0}] +  s/Sqrt[6] *(3*Sin[\[Beta]]^2*opT[1, {2, 2}] +  3*Sin[\[Beta]]^2*opT[1, {2, -2}]))
 and the spectrum showed that there is an additional line in the middle of the spectrum.

I then changed the spin system to SetSpinSystem[{{1, 1}}] and re-simulated this partial Hamiltonian and the middle line disappears. So I was wondering where does the middle line come from?

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