I have always been told that waves interact with objects with a size similar to their wavelength. For example: if you look at your microwave you notice that there is a grid with a size much smaller than the wavelenght (so that they can not pass over), but visible light can pass very easy because its wavelength is much smaller than the size of the grid. It's also known that atoms can not be seen with visible light because their sizes are much smaller than the visible wavelengths (hundreds and hundreds of atoms can be placed in a blue wavelength). I also thought of the hydrogen atom: at n = 1, l = 0 state, the electron does not rotate around the proton (because l = 0) and describes a rectilinear trajectory (crossing the proton!) until it is re-oriented. I asked a professor a few months ago "Why does not the electron collide with the proton?" and he replied me "because you can calculate the associated wavelength for 13.6 eV and you see that it is much larger than the size of the proton (0.84 fm)." And my question is: why do the waves need to have a wavelength similar to the size of objects to interact? Is there a mathematical justification?