  The classical dynamics of collisionless cold dark matter, commonly described
by fluid variables or a phase-space distribution, can be captured in a single
semiclassical wavefunction. We illustrate how classical multi-streaming creates
wave interference in a toy model corresponding to the dynamics of the
Zel'dovich approximation and link it to diffraction optics. Wave interference
dresses the classical skeleton of cold dark matter with universal features akin
to the physical imprints of wavelike (or fuzzy) dark matter. We untangle this
wave interference to obtain single-stream wavefunctions corresponding to the
classical fluid streams, by writing the wavefunction in an integral form. Our
wave decomposition captures the full phase-space information and isolates the
multi-stream phenomena related to vorticity and velocity dispersion. We link
the wave interference features of our system to the standard forms of
diffraction catastrophe integrals, which produce bright caustics in optical
fields analogous to the cold dark matter density field. Our two complementary
descriptions of dark matter wave-fields present rich universal features that
can unlock new ways of modelling and probing wavelike dark matter on the scales
of the cosmic web.
