For the hjydlogen atom (using atomic units) the ground state energy s E = _? and the (unnormalized) ground state wavetunction is '(r) s e a) For W (r) =", calculate H;; and S;; and get E; = H;;/Sy;. b) For Wy(r) = ", calculate H, and S and get E> = Hx/So. ) For (r) = \\W:i(r) + ;'Wa(r) where ; and , are variational parameters, what is E for the optumum values of ; and ,? Note: For part ) you will need to calculate Hi and Si (you already have Hii, S11, H, and S;) and you will need to construct the 2 2 determinant to get the quadratic equation to solve for E (choosing the more negative root). In atomic units, the potential | g : energy operator 1s and the kinetic energy operator is r ~1d 2r drl mn all your integrals. | Make sure to include the 1 from the volume element J"rad_n"r n+l