Problem 2: [30pts] Consider a quantum mechanical system with 3 states and an unperturbed Hamiltonian given by 1 0 0 Ho = E 0 2 0 (3) 0 0 2 a small perturbation is added to this Hamiltonian (i.c. H = Ho + H'). 0 H' = C (1) 2 1 where c is a real number much smaller than E. a) [10pts] Find the basis of eigenstates of the unperturbed Hamiltonian Ho, and the unperturbed energy eigenvalues. b) [10pts] Calculate the first order correction to the energy eigenvalues in perturbation theory. c) [10pts] Find a good basis for degenerate perturbation theory