# Frequency of light photons

1. Aug 20, 2011

### enwa

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 $E = hf$.

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 $c$ and 'phase' velocity $v$.

Refractive index is related to phase velocity by $n = c/v$.

By the above, I think that (A) the wave function for a photon has wavelength $\lambda = 1/f$ 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.

2. Aug 20, 2011

### Bill_K

(C) The wavefunction for a photon shares some of the properties you mentioned for the wavefunction for a particle. It is typically a packet formed from waves having different frequencies. Each of these frequencies corresponds to a certain energy by the usual formula, E = ħω. The photon has a probability distribution in frequency, and a corresponding probability distribution in energy. Even a "pure" spectral line from an atomic transition (e.g. the sodium D line) is not precisely sharp in frequency and energy, it has a finite spread or linewidth. Just as the atomic state it came from has a finite spread in energy.

3. Aug 21, 2011

### enwa

Thanks very much it was fascinating to read about spectral linewidth, apparently arising from energy/time uncertainty principle.

Does anyone know of experiments or theory that back up the idea that the Schrodinger wave function of a photon has frequencies near to the "classical" frequency the light is thought of as having?

4. Aug 21, 2011

### Bill_K

enwa, I should make it clear that a photon does not have a special "wavefunction" ψ in addition to its other properties. A photon is, after all, a quantum of electromagnetism. It is described by the usual E and B fields, and more importantly by the potentials A and φ. When we speak of its frequency, we are talking about oscillations in these quantities.

5. Aug 23, 2011

### enwa

My understanding was that:

• In the classical picture light is made of waves in the EM field and Maxwell gave evidence for this by calculating the speed of light in terms of electric and magnetic permittivity constants.
• In the quantum picture light is composed of photons, which are quantum mechanical particles much like electrons in the sense that they have a Schrodinger wave function.

Based on what you said, it seems like the quantum picture I had is wrong: but I don't know what the correct quantum picture of a photon would be.

6. Aug 23, 2011