If a graph is plotted varying ( E 1 − − E 2 ) along the horizontal axis and E + or E − − along the vertical, we find two branches of a hyperbola (as shown in the figure). The curve asymptotically approaches the original unperturbed energy levels. Analyzing the curves it becomes evident that even if the original states were degenerate (i.e. E 1 = E 2 ) the new energy states are no longer equal. However, if W is set to zero we may find at ( E 1 − − E 2 ) = 0 , E + = E − − and the levels cross. Thus with the effect of the perturbation these level crossings are avoided.