  In the coherent state of the harmonic oscillator, the probability density is
that of the ground state subjected to an oscillation along a classical
trajectory. Senitzky and others pointed out that there are states of the
harmonic oscillator corresponding to an identical oscillatory displacement of
the probability density of any energy eigenstate. These generalizations of the
coherent state are rarely discussed, yet they furnish an interesting set of
quantum states of light that combine features of number states and coherent
states. Here we give an elementary account of the quantum optics of generalized
coherent states.
