  Topological states in quantum materials are defined by non-trivial
topological invariants, such as the Chern number, which are properties of their
bulk wave functions. A remarkable consequence of topological wave functions is
the emergence of edge modes, a phenomenon known as bulk-edge correspondence,
that gives rise to quantized or chiral physical properties. While edge modes
are widely presented as signatures of non-trivial topology, how bulk wave
functions can manifest explicitly topological properties remains unresolved.
Here, using high-resolution inelastic x-ray spectroscopy (IXS) combined with
first principles calculations, we report experimental signatures of chiral wave
functions in the bulk phonon spectrum of BaPtGe, which we show to host a
previously undiscovered twofold degenerate quadruple Weyl node. The chirality
of the degenerate phononic wave function yields a non-trivial phonon dynamical
structure factor, S(Q,$\omega$), along high-symmetry directions, that is in
excellent agreement with numerical and model calculations. Our results
establish IXS as a powerful tool to uncover topological wave functions,
providing a key missing ingredient in the study of topological quantum matter.
