a) Write down the full Hamiltonian for a He atom moving freely in space, i.e., there is no external potential. b) Now assume there is no repulsion between the electrons, what is the full Eigen-function for the He traveling freely through space in the vibrationa ground state? Ignoring the motion of the center of mass what is the ground state energy of the He atom in this approximation? c) Finally again ignoring the motion of the center of mass, excite the He to its first excited state using single electron selection rules, what is the electron configuration and what is the energy of the configuration? What is the wavelength of the transition? There are two possible spin multiplicities that could results after the transition, what are they and how could they occur? this question cannot be found from any resources becuase it's made by our instructor