Do photons have a spectrum like light when they are treated as waves?

If light can be treated as both a particle and a wave, are there things called infrared photons, or ultraviolet photons etc, as there are infrared waves, or ultraviolet waves? Or are photons just packets of energy, as in they have specific quantities of energy that correspond to the different wavelengths of light when taken as a wave. Or is it just that the spectrum only exists if light waves are dispersed, but photons don't get dispersed? The recent photograph of light also doesn't seem to explain this either..or at least I don't see it.

• I can't quite make sense of your last sentence; I think you forgot a word. – Danu Mar 6 '15 at 9:41
• I forgot the word "light", thanks. – tkhanna42 Mar 6 '15 at 9:55
• What photograph? – Oebele Mar 6 '15 at 11:00

are there things called infrared photons, or ultraviolet photons etc, as there are infrared waves, or ultraviolet waves?

Yes, absolutely. Certain aspects of the photon notion can be thought of as even more like a classical wave than even the above. One photon alone can be in a pure quantum superposition of energy eigenstates, or polarization eigenstates. This means that it itself can have a spread of wavelengths. In principle, one can have lone, white photons (although in practice I don't know of any physical processes that can produce pure superpositons of radically different frequencies)! However, there is still a definite - albeit needfully time varying - phase relationship between the frequency components of a "white photon" quantum superposition - it is a pure and not mixed state like "everyday" white light.

How this works is the following. A "lone photon" is simply a state of the quantum electromagnetic field, see the "Quantization of the Electromagnetic Field" Wikipedia article where the number observable is certain to return a measurement of $n=1$.

Moreover, you can define probability amplitude functions of space and time from the quantized electromagnetic field that fulfill Maxwell's equations, which can thus be thought of as the analogue of the Dirac equation for the lone photon. Every classical solution of Maxwell's equations defines a corresponding one photon state and contrariwise. See my answer here for details

• Thanks so much!! I couldn't find this anywhere because I thought it didn't have anything to do with quantum mechanics. (I'm still in high school) – tkhanna42 Mar 6 '15 at 10:00