Consider a vacuum cavity, which admits a radiation mode w. an atom of 2 levels with a separation of hw between its energy levels is prepared in its excited state le), and is sent into the cavity, where it enters at the time t = 0. (a) Write down what is the wave function for the atom inside the cavity. (b) Plot the probability of finding the atom in its ground state, and find at what time T_f a photon is deterministically deposited on the cavity. What is the wave function at this time? (c) The photon in the cavity has a finite half-life, t_f , so the amplitude probability of having a photon in the cavity decays according to 1) e-t/2T 1) From T_f, which we now take to be t = 0 (i.e., we reset the clock), to a time T