1. The problem statement, all variables and given/known data I have the matrix form of the Hamiltonian: H = ( 1 2-i 2+i 3) If in the t=0, system is in the state a = (1 0)T, what is Ψ(x,t)? 2. Relevant equations Eigenvalue equation 3. The attempt at a solution So, I have diagonalized given matrix and got the eigenvalues: 2+√6 and 2-√6. I am suspecting that these are not good, since I can't get eigenvectors I can use. When trying to calculate eigenvectors, I get: a = 1 and b=(-1+√6)/(2+i). This is the one I got when I used 2+√6 but after that I didn't even try with the other eigenvalue since it will be similar. I don't know what to do with those and don't know how to normalize them. Also, even if I knew how to get correct eigenvectors, I am not sure how to proceed and get Ψ(x,t).