# Photon energy depends on frequency (and/or amplitude)? [duplicate]

I know there are already some similar questions like Amplitude of an electromagnetic wave containing a single photon but I can't get my head around it since the answers there seem not to fit very precisely to the question: What is the amplitude of a single photon? I know the energy of a photons depends strictly on its frequency and light is described by electromagnetic waves. Are (single) photons also seen as electromagnetic waves? If so, what does it amplitude then tell? Thank you!

• The intensity tells how many photons are in a beam of light. As intensity is the energy per unit area and unit time it makes sense as average for dealing with light beam rather than single photons. The latter are counted, in practice. Commented Jan 31, 2018 at 14:36
• This is a very big question, with lots of discussion, as you noted. Briefly: a photon are not seen as a wave itself, but rather as an excitation of a wave. Roughly speaking amplitude is related to the number of photons. Commented Jan 31, 2018 at 14:37
• I see you perhaps mean if there is an electromagnetic wave for a single photon? The substance is the same but I cannot answer to this way of seeing your question. Surely duplicate in both viewpoints Commented Jan 31, 2018 at 14:40
• @garyp But what is the amplitude in case of a single photon since photons are electromagnetic waves (?)
– Ben
Commented Jan 31, 2018 at 16:24
• It is clear for me and as from other answers till we get to few or a single photon. In the latter case forget a wave train. The answer is tricky to me but should be here in SE. These next days I will reformulate the Q to get kind of strict yes or no. For the details we can then dig. Commented Jan 31, 2018 at 16:34

The energy of light wave is not simply it's frequency component - it is both its frequency and amplitude.

But as with any wave, amplitude is a different quality than frequency, and the two are not completely interchangeable in their effects (even though a wave with high-amplitude and low-frequency may carry the same or more energy as a wave with low-amplitude and high-frequency) because of the effects of resonance (which is somewhat related to inertia).

Consider when your car bumps over a pothole - even a relatively shallow pothole might break wheels and almost knock your fillings out. That's a high-frequency, low-amplitude shock.

And yet you may drive up and down a mountainside comfortably (even though the amplitude of that movement involves orders of magnitude more energy being borne by the car through its wheels and suspension, it is so diffuse over time that it is insufficient to disrupt the physical integrity of the car or your body, which simply rides the wave rather than being shattered by it).

There is no way to substitute amplitude to achieve the same effect that frequency has - excessive amplitude would compromise the superstructure of the car rather than shocking it's components or passengers.

The same is true of atoms, that at too low a frequency of light, they may be temporarily perturbed by such light but it is insufficient to affect their integrity and cause (for example) the photoelectric effect, and at too high an amplitude, the solidity of the superstructure which is composed of the atoms would be compromised before the individual atoms were.

• Thanks for the vivid explanation regarding frequency and amplitude! But still the question remains: What is the amplitude of a single photon? The energy of a photon is E=hv, therefore its energy should only depend on the frequency? Where's the amplitude?
– Ben
Commented Jan 31, 2018 at 16:28
• Steve this is clear. The juice of the Q is more or less "is a single photon described by a electromagnetic wave? An oscillator absorbing it it is supposed to do it by virtue of frequency. By is seem more a kind of solitonic wave, being alone. Tricky. Naively i would take the wave of 1 mole of photons and divide by Na....... Commented Jan 31, 2018 at 16:41
• This answer is ok for the classical picture of EM radiation, but not the quantum mechanical picture, in which one has to carefully distinguish between energy, power, and intensity. Commented Jan 31, 2018 at 16:45
• @Ben, the answer is that the Planck constant stands in for the "amplitude" when the photon is conceived as a particle (i.e. all photons have a constant amplitude, and the only variable about them is their frequency). Obviously, the aggregate amplitude can be increased by increasing the number of photons involved, but what this does say is that the amplitude of light must always be an integer multiple of the Planck length (i.e. it "steps"), whereas the frequency of light is infinitely variable. Commented Jan 31, 2018 at 17:00
• @Ben, there isn't such a thing as a "photon", in the sense of a little particle with certain properties. That's why I say I've fallen into error by adopting that approach in order to explain amplitude. What you really have is a wave-front, but instead of a wave-front with an even amplitude at all points (which continuously decreases as the wave propagates out), you actually have localised peaks (with an amplitude that is an integer multiple of the Planck constant), and as the wave-front spreads, these peaks do not decrease (below 1), but instead the empty space between them merely increases. Commented Feb 1, 2018 at 15:44