(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is an Hamiltonian operation which is given by

(2 1 1)

(1 2 1) = H ; 3-by-3 matrix

(1 1 2)

And let's have an arbtrary eigenvector

(a)

(b) = v ; (3x1) matrix

(c)

Then, from the characteristic equation, the eigenvalues are 1,4. Here eigenvalue 1 is

repeated one.

2. Relevant equations

Now, my question arises. I know that the eigenvectors that corresponds to eigenvalue 1 is two and both are orthgonal to each other. However, I can't find any of them because when

I substitute eigenvalue into 1, I get a kind of meaningless(?) equation,

(2 1 1) (a) (a)

(1 2 1) (b) = (b)

(1 1 2) (c) (c) .

And it gives 3-equivalent equation, a+b+c = 0

I couldn't determine any relation between a,b,c.

3. The attempt at a solution

So I quess that do I have to choose a,b,c satisfying the condition a+b+c=0

but still problem doesn't disappear beacuse there would be a lot of soulutions....

What did I wrong?????

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# Homework Help: Repeated Eigenvalue Problem

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