. A simple atom has a ground state |g) and an excited state |e), with energies E, :E = E, respectively.= 0 and (a) Draw the energy level diagram, and

label all relevant aspects. (b) The atom is prepared in the state |\psi\rangle=\sqrt{\frac{2}{3}}|g\rangle+\sqrt{\frac{1}{3}}|e\rangle Calculate the probability of finding the atom in the excited state Je). (c) Calculate the expectation value for the energy of the atom in state psi The time evolution of the atom is governed by the Hamiltonian H, with H=E_{g}|g\rangle\left\langle g\left|+E_{e}\right| e\right\rangle\langle e| Calculate the state of the atom at time t = T, given that the atom is in state |) at time t = 0. At time T we measure whether the atom is in the state |+\rangle=\frac{|g\rangle+|e\rangle}{\sqrt{2}} \quad \text { or } \quad|-\rangle=\frac{|g\rangle-|e\rangle}{\sqrt{2}} Calculate the probability of finding the atom in state |+), and sketch this probability as a function of time.