What is the fundamental reason why the allowed energies of electrons are quantized? I did some research on the web before posting this and what I found seems to link this to the wave-like behaviour of electrons. That is, if electrons could hypothetically exist within the band gaps of the atom, then the electron wave would effectively cancel itself out (like standing waves which effectively give no waves between the various harmonics). Therefore, as it would cancel itself out it cannot exist there. Is this an accepted explanation? I thought that the allowed energy states also depend on the values of the various quantum numbers of the electrons?