For the hydrogen atom (using atomic units) the ground state energy -1 2 is E = and the (unnormalized) ground state wavefunction is Y(r) =e a) For Y(r) = 0.5, calculate H1 and S11 and get E = H1/S11. -2.0r b) For Y(r) =e0r, calculate H22 and S22 and get E = H22/S22. = E2 c) For Y(r) c(1) c22(r) where c and c are variational parameters, what is E for the optimum values of c and c? Note: For part c) you will need to calculate H12 and S12 (you already have H11, S11, H22, and S22) 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 energy operator is 7 and the kinetic energy operator is 2. Make sure to include the r from the volume element -1 d 2r dr d dr in all your integrals. -1 00 Fredr 0 = n! n+1