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I found a partial answer in the documentation centre, but would like to expand on it and know how can I fit multiple sets of data and extract the parameters from them. It is an eigenvalue problem - We have a 3x3 matrix

{{E(θ)-E, V1, V2}, {V1, E1-E, 0}, {V2, 0, E2-E}}

We set Det(matrix)=0 to get the $E$ eigenvalues, though the E[θ] = E0*(1-(Sin[θ]/neff)^2)^(-0.5). So the eigenvalues will change with angle. Now I have 3 data sets to fit the 3 solutions of my problem and have to extract the free parameters $V1,\,V2,\,E0,\,neff$ that best fit my data. Any suggestions ?

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Why don't you try to expand on the existing solution as you have pointed out and then if you are on a bumpy road ask again ? –  Sektor Mar 7 at 11:30
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