The vibrational excitations of crystalline solids corresponding to acoustic or optic one phonon modes appear as sharp features in measurements such as neutron spectroscopy. In contrast, many-phonon excitations generally produce a complicated, weak, and featureless response. This talk will discuss time-of-flight neutron scattering measurements for the binary solid uranium nitride (UN), showing a series of well-defined, equally-spaced, high energy vibrational modes in addition to the usual phonons. The spectrum is that of a single atom, isotropic quantum harmonic oscillator and characterizes independent motions of light nitrogen atoms, each found in an octahedral cage of heavy uranium atoms. This is an unexpected and beautiful experimental realization of one of the fundamental, exactly-solvable problems in quantum mechanics that is taught in an introductory undergraduate course. There are also practical implications, as the oscillator modes must be accounted for in the design of generation IV nuclear reactors that plan to use UN as a fuel.