Are deBroglie waves transverse or longitudinal? Can they be polarized? What about the deBroglie wave of a ground state neutral spin-zero Helium 4 atom? What experimental evidence do we have that supports the detailed nature of a deBroglie wave? I have always assumed that deBroglie waves were mathematically identical to electromagnetic waves, but I just realized there is no basis for this assumption, and in fact it must be false, unless there is an analogue to both the magnetic and the electric components of the electromagnetic wave. So what does a deBroglie wave "look like"?
The de Broglie wave "looks like" the wave function of quantum mechanics. Because it is simply anothe name for it. In particular, it is defined on the configuration space, the space of all possible configurations of the universe.