Problem 4+ Use a trial function y = re"", with a as a variational parameter to calculate the ground state energy of the H atom.+ Hints:+ 1) Normalize the wave function using spherical coordinate system 2) Find the expression for the energy as function of parameter @. Use the Hamiltonian operator as for H atom, easiest is to employ atomic units: + H = R+V = - 2 a 1(1 + 1) 1 Far + 1-2 Assuming that the ground state is a 1s orbital - the / = 0. This leads to a smaller Hamiltonian:+ H = R+ V =- 2 a NI 3) Evaluate the derivative of energy with respect to parameter a. Determine the best value of a by solving the equation: - = de =0.+ 4) Write down the wave function and energy for the obtained value of a.+ The following standard integrals might be useful:+ xhe Wax = 4! 24 3 -20 dr = 72 )5 3205 3! 3 Be Car dr = (24 )4 2 nag 2ar dr = (2a )3 O 1 (20 )2 40x2