10.14 The three-fold degenerate energy level of the hydrogen atom, with the eigen vectors |n = 2, e = 1, m =+1,0), is subjected to a perturbation of the form

V = b(r? -y). Use degenerate perturbation theory to deter-mine the zero order eigenvectors and the splitting of the energy levels to the first order in b. (You need not evaluate the radial integrals that occur in the matrix elements of V, but you should determine which arevero, which are nonzero, and which nonzero matrix elements are c qual.)

Fig: 1