# Photon Energy & Wave Amplitude

• B
• jeremyfiennes
In summary, the energy of a photon is determined by its frequency, which is a wave property. However, the energy also depends on the amplitude of the wave. This can be a common misunderstanding due to the misconception that individual photons can be treated as waves. In reality, the electromagnetic field is what is quantized and the energy of a single photon is always constant.
jeremyfiennes
TL;DR Summary
Where does a photon's wave amplitude enter into its energy equation?
A photon's energy is E=hv where v, the frequency, is a wave property. Particles don't have frequencies. But a wave's energy also depends on its amplitude. Where does this come into the energy relation?

jeremyfiennes said:
a wave's energy also depends on its amplitude. Where does this come into the energy relation?

Wave amplitude corresponds to the expectation value of photon number (more precisely, to the square root of it). So in the photon model it has nothing to do with the properties of individual photons; it's just how many photons there are.

BvU
This seems to be the typical misconception arising from the misunderstanding that one could treat photons with a wave function as in non-relativistic Schrödinger quantum mechanics. That's not the case. The electromagnetic field is what has to be quantized, because photon number is not conserved but photons can easily be created and destroyed in interactions of charged particles.

The free field, describing asymptotic free states is normalized such as to obey the canonical commutation relations in, say, the Coulomb gauge (or for free fields the "radiation gauge" following from it). Then you can define momentum-eigenmodes of single free photons and build the entire Fock space from the photon-number eigenstates. The total energy density is then given as an expectation value with respect to the states. A single photon in a single-frequency mode always has the energy ##\hbar \omega##, no more no less, and all you can say about this photon is the probability that it's detected by some detector. It's always detected as a whole or nothing.

## 1. What is photon energy?

Photon energy refers to the amount of energy carried by a single photon, which is the smallest unit of light. It is directly proportional to the frequency of the light wave, meaning higher frequency light has higher photon energy.

## 2. How is photon energy related to wave amplitude?

Wave amplitude refers to the height of a light wave, and it is directly related to the intensity or brightness of the light. As the amplitude increases, the number of photons also increases, leading to higher photon energy.

## 3. What is the formula for calculating photon energy?

The formula for calculating photon energy is E = hf, where E is energy, h is Planck's constant (6.626 x 10^-34 joule seconds), and f is frequency. This formula shows the direct relationship between photon energy and frequency.

## 4. How does changing the frequency of light affect photon energy?

As mentioned earlier, photon energy is directly proportional to frequency. This means that as the frequency increases, photon energy also increases. This is why higher frequency light, such as ultraviolet or x-rays, can be more damaging to living organisms than lower frequency light like radio waves.

## 5. Can photon energy be converted into other forms of energy?

Yes, photon energy can be converted into other forms of energy, such as heat or electricity. This process is known as the photoelectric effect, where photons transfer their energy to electrons, causing them to be ejected from a material and creating an electric current.

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