The Hamiltonian operator for a two-state system is given by, H = (| l> <1 | |2 > < 2| + |1 >

The Hamiltonian operator for a two-state system is given by, H = α (| l> <1 | – |2 > < 2| + |1 > < 2| + |2 > < 1|), where a is a number with the dimension of energy. Find the energy Eigen values and the corresponding energy eigenkets (as linear combinations of |1 > and |2 >).