1. The problem statement, all variables and given/known data The system described by the Hamiltonian [tex] H_0[/tex] has just two orthogonal energy eigenstates, |1> and |2> , with <1|1>=1 , <1|2> =0 and <2|2>=1 . The two eignestates have the same eigenvalue , E_0: H_0|i>=E_0|i>, for i=1 and 2. Now suppose the Hamiltonian for the system is changed by the addition of the term V, given H=H_0+V. The matrix elements of V are <1|V|1> =0 , <1|V|2>=V_12, <2|V|2>=0. a) Find the eigenvalues of the new Hamiltonian, H , in terms of the quanties above b) Find the normalized eigenstates of H in terms of |1> , |2> and the other given expressions. 2. Relevant equations 3. The attempt at a solution a) I don't know how to begin this problem but I guess I will start by plugging in the values for H_0 and V: H=H_0+V=<1|1>+<1|V|1>=1+0=1 for the first value of H_0 and the first value of V. don't you find the eigen value by writing out this expression: det(H-I*lambda)=0? I have kno w idea.