What kind of wave is associated with particles , in wave particle duality?
This is a really good question. There are several kinds of wave involved here. First, there are the probability functions that, when drawn out, appear as normal shaped translational waves that are high in the middle and trail out on either end, like a bell curve. But these are three dimensional when looking at electrons and their locational probabilities. Thus you need to sort of rotate the two-dimensional bell curve to make it three dimensional, which forms a shell around the atomic core. In fact, the shape may be highly skewed so that the hump in the curve is off to one side or the other. Second, the are the translational waves of the energies for the individual particles. These, too, appear like wavey bell curves. What they are is multiple waves that introduce destructive interference, which is why they stay grouped tightly together and appear to act as particles…quanta. This is the wave in the well-known E = hf; where E is the energy of the quantum, h is Planck’s constant, and f
