The photoelectric effect is the case where photons of light eject electrons from a sheet of metal like interacting partials are supposed to behave. The Davission-Germer experiment has an electron beam is aimed a nickel crystal in whith the resulting scattering has peeks and valise do to diffraction.
The wave length of a particle's wave is l = h / p. Where l is the wave length, p is momentum h is Planck's constant Now this relationship is just the first part of wave particle duality. The actual wave function is denoted by Y (Psi). While the exact formula varies with the situation, the wave function is always a complex number. It is related to the probability of finding the particle at a given point in pace.
The probability of finding a partial at a given point in space is denoted by |Y(x)|2 also denoted by Y* Y where the complex number is Y = A + iB and the complex conjugate: Y* = A – iB The over all space the probability density = 1.
In conclusion matter behaves as both particles and waves. The wave nature is related to the probability of finding a particle at a given location at a given time.