# Plot the eigenvalues of a spin-1 system in a magnetic field?

Posted 8 months ago
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 Hi,so my general goal is to calculate the eigenstates of a spin-1 system in a magnetic field which is not parallel to the spin axis. Therefore the system has B and α as variables.This is what I got so far: Manipulate[ Plot[{\[Lambda]1, \[Lambda]2, \[Lambda]3} = Eigenvalues[ h*D1*(Sz)^2 + g*\[Mu]B*B*Cos [\[Alpha]]*Sz/h + g*\[Mu]B*(Sqrt[B^2 - (B*Cos [\[Alpha]])^2]*Sx + By*Sy)/h + h*E1*(Sx.Sx - Sy.Sy)], {B, 0, 0.040}, GridLines -> {{{2.87*10^9, Red}}}, PlotRange -> {{0, 0.04}, {-0.5*10^9, 4*10^9}}, PlotRangeClipping -> True, Frame -> True], {\[Alpha], 0, Pi/2}] with the following constants used: D1 = 2.87*10^9 1/h; E1 = 0.005*10^9 1/h; g = 2.00231930436182; \[Mu]B = 9.274009994*10^(\[Minus]24); h = 6.626070040*10^(\[Minus]34); By = 0 and S are the spin-1 Pauli matrizes Sx = 1/Sqrt[2] * ( { {0, 1, 0}, {1, 0, 1}, {0, 1, 0} } ); Sy = 1/Sqrt[2] * ( { {0, -I, 0}, {I, 0, -I}, {0, I, 0} } ); Sz = ( { {1, 0, 0}, {0, 0, 0}, {0, 0, -1} } ) Is their a way to do a similar plot but with λ1-λ3 and λ2-λ3?Thanks for your help,Stefan
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Posted 8 months ago
 define a function which gives the eigenvalues as a function of alpha and use that to plot the differences