  The momentum dependent lineshape of the out-of-phase oxygen vibration as
measured in recent neutron scattering measurements is investigated. Starting
from a microscopic coupling of the phonon vibration to a local crystal field,
the phonon lineshift and broadening is calculated as a function of transfered
momentum in the superconducting state of YBa$_{2}$Cu$_{3}$O$_{7}$. It is shown
that the anisotropy of the density of states, superconducting energy gap, and
the electron-phonon coupling are all crucial in order to explain these
experiments.
