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slam7211
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Homework Statement
sorry about the lack of LaTex but I don't know how to do bra-ket notation in tex
vectors |1> and |2> are a complete set of normalized basis vectors.
the hamiltonian is defined as |1><1|-|2><2|+|1><2|+|2><1| find the eigenvalues and eigenvectors in ters of |1> and |2>
Homework Equations
for a normal matrix eigenvalues are
Det(A-Iλ)=0 solve for λ
Eigenvectors are then
A*v=λv
The Attempt at a Solution
I tried just making up 2 generic 1X2 vectors and plugging it into mathematica, but its ugly and I am assuming its not what they want, is there some stupid trick I am missing here?
If the first sign in the hamiltonian was + instead of minus I know the first set of terms would equal 1 but its minus so I am just lost here