Consider two electrons in a one-dimensional box of length l. the potential energy is zero inside the box and infinite outside of it. the potential energy of the electron-electron interaction is v(x_1, x_2). a) first, assume that v(x_1, x_2) = 0. find the ground state energy and write down the ground state wave function considering spatial and spin state symmetry. b)now v(x_1, x_2) = l v_0 delta (x_2 - x_1). assuming that v_0 is small find the correction to the ground state energy.