I can't quite seem to understand wave particle duality. Every particle has a characteristic wavelength according to de Broglie. Is this the wavelength for the solution to the schrodinger equation for that particle? Take light for example, the wavelength of light corresponds the the wavelength of the electromagnetic wave, which is a physical wave. However, this is not the same wave as the solution to the schrodinger equation (is it?) since the schrodinger equation gives complex (and hence non-physical) solutions. However, I know that de Broglie came up with his equations by simply reversing Einstein's equation for the photoelectric effect. So what kind of waves are particles? Is a photon both a quantum mechanical matter wave and an electromagnetic wave at the same time? Do particles in general exist as physical waves or only as imaginary waves relating to the probability of finding the particle at that point, or both of these at the same time?