It was now 1957, and Gordon had been a post-masters student at Columbia since 1949. Gordon had told Townes about these ideas, and in fact had gotten him to sign the laboratory notebook in which they had been outlined. Gordon at once figured out that population inversion would enable him to construct a maser of any material, whereas the original Townes et. Since I feel that the concept of coherence is one of the least understood aspect of physics, let me put in my two cents' worth. In superposing quantum states, one adds the amplitudes when there are no possibilities, even in principle , of distinguishing the states.
Examples are two-slit diffraction or elastic scattering of neutrons by a crystal lattice.
When the sum of amplitudes is squared to give a probability, interference terms arise. We call this diffraction. In stimulated emission, photon 1 impinges on an atom, and stimulates the emission of photon 2, so now there are two photons. So these two photons are indistinguishable, and in particular they have precisely the same frequency. We say that they are coherent.