Understanding de Broglie Wavelengths

[nsang]

I understand the derivation and calculation of de Broglie wavelengths. What I don't understand is what exactly they are. What does the wavelength of a particle mean? Does it mean the wavelength of its probability wave, or some other kind of wave?

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, what quantity is oscillating in their wave?

Thanks!

 

[Jano L.]

That depends on the theory you use to interpret the equation. For de Broglie, it meant something like this:

Imagine point-like particle whose velocity is determined by a kind of guiding wave (pilot-wave theory). The wave behaves similarly to common kinds of wave, it can propagate, interfere and form some pattern of maxima and minima. If the particle is at place where the wave amplitude changes much, the velocity of the particle is large. If the amplitude has plateau, the particle there does not move much.