If E 1 and E 2 are the energy levels of the system, such that E 1 = E 2 = E , and the perturbation W is represented in the two-dimensional subspace as the following 2×2 matrix W = [ 0 W 12 W 12 ∗ ∗ 0 ] . then the perturbed energies are E + = E + | W 12 | E − − = E − − | W 12 |