Undergrad How do we interpret an EM wave using Quantum Mechanics?

[calinvass]

I know that if the intensity of a light beam with of a certain frequency varies it means the number of photons the light beam is composed of varies and not the individual photons energy. That would mean the E and B field amplitudes vary. This would mean that that the amplitudes of the E and B fields are given by the number of photons in the wave. However, I can also think that within the wave in the area where there is an E field maximum amplitude there are more photons which I think doesn't make sense.
When two EM waves overlap (same phase) the E and B fields add up. But the number of photons is preserved (they don't merge) because if in a pulse of light the photons energy is preserved the number of photons,!carrying the smallest quantum of energy, will increase. That can mean that there are two types of amplitudes. One that is discrete and gives the energy of the photon and the other that gives the number of the photons. In classical physics and when using radio waves they seem to mean the same thing.

 

[Lord Jestocost]

Don't think of a light beam as composed of photons which are traveling around like "particles". Quantization of electromagnetic radiation means that the field energy can only be changed by integer numbers of „energy portions“ (called photons) of amount hν, where ν is light frequency and h Planck's constant.

 

[calinvass]

Thank you. That is clear, but what about the electric / magnetic field peak amplitude? If we have two light pulses of the same length and diameter but different frequencies and the same total energy (the average energy density is the same), what will be the difference in the E or B field peak amplitudes? Let's assume the source is linearly polarised and coherent.

 

[calinvass]

Don't think of a light beam as composed of photons which are traveling around like "particles". Quantization of electromagnetic radiation means that the field energy can only be changed by integer numbers of „energy portions“ (called photons) of amount hν, where ν is light frequency and h Planck's constant.

The photoelectric effect shows there is more than that. Electrons seem to only absorb one photon at a time. Even if we increase the light intensity, and we can have more photon density, the electrons don't seem to jump on higher levels or get knocked out from the orbit. That would mean they are distributed inside the beam as if they were particles.

 

[PeterDonis]

I know that if the intensity of a light beam with of a certain frequency varies it means the number of photons the light beam is composed of varies and not the individual photons energy.

Heuristically, yes; but you should be aware that "the number of photons" itself is not definite for most light beams. That is, the quantum state of most light beams is not an eigenstate of the photon number operator. This applies in particular if you are talking about states where concepts like "electric field" and "magnetic field" are useful. See below.

That would mean the E and B field amplitudes vary.

If we are in a quantum context, you have to be careful because E and B fields are not the fundamental quantum entities here. The quantized electromagnetic field is. The E and B fields are operators, and not the same ones as the photon number operator--that is, eigenstates of the E and B field operators (i.e., states which have a definite amplitude for the E and B fields) are not eigenstates of the photon number operator (so they don't have a definite photon number).

That means that you can't talk about a given state of a light beam as having a definite photon number and a definite amplitude for the E and B fields. You have to pick one or the other.

This would mean that that the amplitudes of the E and B fields are given by the number of photons in the wave.

No, it doesn't. See above.

When two EM waves overlap (same phase) the E and B fields add up.

No, the underlying quantum fields add (because the quantized electromagnetic field is a linear field). But that is not the same as the E and B fields adding.

The rest of your post just builds on the above errors.

 

[PeterDonis]

The photoelectric effect shows there is more than that. Electrons seem to only absorb one photon at a time.

You aren't disagreeing with @Lord Jestocost here; you're just restating what he said. An electron absorbing a photon, when put into proper quantum field language, means: a quantum of energy is transferred from the quantized electromagnetic field to the quantized electron field. The amount of energy in the quantum depends on the frequency of the light, which is a property of the quantized electromagnetic field.

 

[vanhees71]

The photoelectric effect shows there is more than that. Electrons seem to only absorb one photon at a time. Even if we increase the light intensity, and we can have more photon density, the electrons don't seem to jump on higher levels or get knocked out from the orbit. That would mean they are distributed inside the beam as if they were particles.

The photoeffect doesn't demonstrate the quantum nature of the electromagnetic field at all. It can be well understood in the semiclassical approximation, i.e., a classical em. wave interacting with a (bound) electron:

https://www.physicsforums.com/insights/sins-physics-didactics/

The most simple phenomenon you really need the quantization of em. field for is "spontaneous emission" (discovered already 1917 by Einstein before the advent of modern QT, first described by quantization of the em. field by Dirac in 1927).

 

[calinvass]

If we are in a quantum context, you have to be careful because E and B fields are not the fundamental quantum entities here. The quantized electromagnetic field is. The E and B fields are operators, and not the same ones as the photon number operator--that is, eigenstates of the E and B field operators (i.e., states which have a definite amplitude for the E and B fields) are not eigenstates of the photon number operator (so they don't have a definite photon number).

That means that you can't talk about a given state of a light beam as having a definite photon number and a definite amplitude for the E and B fields. You have to pick one or the other.

It looks similarly to the uncertainty principle. But I 'm not sure how much impact has when analysing a light pulse of high energy and very high number of photons.