The meaning of the De Broglie wavelength of a particle is entirely unclear to me. 1. To which kind of wave does the wavelength belong? To the wave that determines how likely the free particle is to show up in certain places (probabilities as squared amplitudes)? If yes: 2. Why is the wavelength inversely related to the momentum of the particle? Why do the positions where the particle could show up get more densely spaced if the speed of the particle is higher? 3. What does such a wave that has equally high amplitues all over the universe even mean? The picture of a particle with a certain momentum (even with some probabilistic variance) and that of a probability distribution of places that says that it is equally likely that the particle shows up here or 2000 miles from here just don't fit together. (I do realize that usually wave packets are used to describe particles; it's just not clear to me what the meaning of De Broglie waves then is.) I would be happy if someone could clear up my thoughts a little. Thanks!