QM states of a system are described by linear super positions of two linearly independent state vectors psi1 and psi2. These two states are normalized but are NOT orthogonal to each other. A hermitian operator A actes on the two states in the following way.
A|psi1> = 5|psi1>+3|psi2>
A|psi2> = -3|psi1> - 5|psi2>
Determine the eigenvalues and properly normalized eigenvectors of A.
The Attempt at a Solution
I attempted to introduce a general state |phi> = C1|psi1> + C2|psi2>, act A on |phi> and apply the normalization condition on |phi> to determine C1 and C2 but have gotten nowhere. I have found the value of <psi2|psi1>. Thanks for your help.