In the electromagnetic picture, different frequencies of light waves produce different strengths of diffraction/refraction. In the quantum picture, a photon's energy corresponds to its frequency by the Planck constant [itex]E = hf[/itex]. The solution of Schrodinger's equation for a free particle (which we can model a photon with) gives a continuous spectrum of non-normalizable waves, to get a physical wave function a normalizable superposition is formed. These have both 'group' velocity [itex]c[/itex] and 'phase' velocity [itex]v[/itex]. Refractive index is related to phase velocity by [itex]n = c/v[/itex]. By the above, I think that (A) the wave function for a photon has wavelength [itex]\lambda = 1/f[/itex] as opposed to the alternative (B) the frequency of a photon is an intrinsic quantity much like spin. Is (A) correct, and if so how is this known? But maybe I am wrong, if (B) or some alternative is true please tell me where my reasoning is wrong and how correct the correct model of a photon is known. Thanks very much.