I have a hard time understanding some very fundamental things about matter waves. To start with, the basic question is what are these De Broglie waves? Is it just a pure mathematical concept that describes probability of the particle to be in a certain place or is it some property of space? As I understand, there is no really a disturbance traveling in the medium around the particle - the De Broglie wave has only a probabilistic nature. But for example, in electromagnetism we have the electromagnetic waves which are propagating disturbances in an electric/magnetic field. At the same time, they are also describing the probability of a photon to be in a certain place. So is this a coincidence that electromagnetic waves happen to be both real physical disturbances and at the same time a "tool" that tells you the probability of photon to be in certain point in space? Are the De Broglie waves essentially the same, except that they aren't physically present (again, pure mathematical tool)? One more thing - often as an example of the wave nature of particles (say, electrons), books come up with some diffraction experiment. And I'm okay with that. However, in Bohr model of the atom, one way to prove the quantization of angular momentum is by showing that instead of electron orbit we have a standing wave. Thus, 3 questions arise: 1) There is no diffraction when electron orbits around the atom (i guess). It's like there is no diffraction when you turn on laser and just see a straight beam of photons moving. In order to see the wave properties, you have to do some sort of diffraction/interference experiment. Then why we are allowed to say that an electron behaves like a wave even when it orbits the atom? 2) Does it imply that an electron behaves like a wave no matter whether it goes through slit or no? So, in general we never can know the precise location of the electron? Even if we fire it in a very precise direction (no atoms involved)? 3) Do these "orbit-waves" describe the probability of an electron to be in certain place in the orbit or do they describe the probability of an electron to be in a certain orbit?