a. Set up the Hamiltonian operator for the system of an electron interacting with a fixed nucleus of atomic number Z, such as singly ionized helium with Z=2.
b. Based on the Hamiltonian in part (a), what would be the corresponding energies and solutions to the corresponding radial equation? Provide the general expressions.
c. Calculate the average distance of the electron from the nucleus in the 1s state of this system?