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This question already has an answer here:

This is the code I have:

ϵs = -13.6;
ϵso = -29.1;
ϵp = -14.1;
ssσ = -7.20;
spσ = 9.46;

θ = ((π - β)/2);

Hmatrix0[θ_] = 
{
  {ϵs, 0, ssσ, Cos[θ]*spσ, -Sin[θ]*spσ, 0}, 
  {0, ϵs, ssσ, -Cos[θ]*spσ, -Sin[θ]*spσ, 0}, 
  {ssσ, ssσ, ϵso, 0, 0, 0}, 
  {Cos[θ]*spσ, -Cos[θ]*spσ, 0, ϵp, 0, 0}, 
  {-Sin[θ]*spσ, -Sin[θ]*spσ, 0, 0, ϵp, 0}, 
  {0, 0, 0, 0, 0, ϵp}
}

Eigenvalues[Hmatrix0[θ]]

This is a sample of one of the eigenvalues:

Root[(38319.6 + 0. I) - 130827. Cos[β] - 116527. Cos[2 β] + (120228. - 9278.49 Cos[β] - 4004.37 Cos[2 β]) #1 + (29612. + 9.09495*10^-13 Cos[β]) #1^2 + 2480.29 #1^3 + 84.5 #1^4 + 1. #1^5 &, 1]

I wish to plot the eigenvalues as a function of beta as it ranges from $\frac{\pi}{2}$ to $\pi$ but I don't know what those hashes are and putting N[hmatrix0[$\beta$]] doesn't work.

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marked as duplicate by J. M. 13 hours ago

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
You forgot to define \[Beta]; N will work if it is numerically defined. – Mr.Wizard Mar 14 '13 at 5:36
2  
Also see: mathematica.stackexchange.com/a/13768/121 – Mr.Wizard Mar 14 '13 at 5:36
    
@Mr.Wizard, how do I make beta a variable that ranges from pi/2 to pi? – user17338 Mar 14 '13 at 5:44
    
@Mark please make that an answer; there's no point sticking it in the question like that. :-) – Mr.Wizard Mar 14 '13 at 5:57
1  
Those aren't "hashtags" - look up Slot in the documentation. – Verbeia Mar 14 '13 at 5:57
up vote 9 down vote accepted

First, you need to keep your $\theta$s and $\beta$s straight. Let's define the matrix in terms of $\theta$ and worry about the relationship with $\beta$ in a bit.

epss = -13.6;
epsso = -29.1;
epsp = -14.1;
sssigma = -7.20;
spsigma = 9.46;
Hmatrix0[theta_] = {
  {epss, 0, sssigma, Cos[theta]*spsigma, -Sin[theta]*spsigma, 0}, 
  {0, epss, sssigma, -Cos[theta]*spsigma, -Sin[theta]*spsigma, 0}, 
  {sssigma, sssigma, epsso, 0, 0, 0}, 
  {Cos[theta]*spsigma, -Cos[theta]*spsigma, 0, epsp, 0, 0}, 
  {-Sin[theta]*spsigma, -Sin[theta]*spsigma, 0, 0, epsp, 0}, 
  {0, 0, 0, 0, 0, epsp}
};

Now, we can make your plot as follows.

Plot[Evaluate[Eigenvalues[Hmatrix0[(Pi - theta)/2]]],
  {theta, Pi/2, Pi}, PlotStyle -> Thick]

enter image description here

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