- #1
J.Asher
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Homework Statement
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.
Homework 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.
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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