I understand the derivation and calculation of de Broglie wavelengths, but what exactly does the wave of a particle represent? What does the wavelength of a particle mean? I'm assuming it's not the wavelength of its probability wave because then there would be no uncertainty in momentum, unless it represents the average wavelength.

The idea of wave-particle duality for EMR makes sense to me in that it can be seen as oscillating changes in energy (a wave), and as photons from the photoelectric effect. But with particles, I don't understand what quantity would be oscillating in their wave.

Thanks!