  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. Here we present time-of-flight
neutron scattering measurements for the binary solid uranium nitride (UN),
showing 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. 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.
