# Learned that light is electromagnetic waves

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Until now I've learned that light is electromagnetic waves. I haven't learned about photons yet, but I'm guessing that photons are waves according to the electromagnetism theory (or quantum mechanics?, or both?).
My question is "when do you consider photons as particles"? Particles in the sense of particles in classical mechanics I think I'm meaning. Is my question too vague?
I've heard about a duality wave/particle of photons, but I've no idea when photons can be considered as particles and if they are particles under certain circumstances. Thanks for any enlightenment.

You dont consider them as particles; and you dont consider them as waves. When you think about light consider it as something that has wave-like, AND particle-like properties. however it is not both, and it is not either. :)
Now you're probably more confuzzled!

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You dont consider them as particles; and you dont consider them as waves. When you think about light consider it as something that has wave-like, AND particle-like properties. however it is not both, and it is not either. :)
Now you're probably more confuzzled!

Yes I'm more confused!
I'm having a hard time trying to understand Maxwell's equations and their solutions. For example if we take the ones in vacuum, they have non trivial solutions that are in fact electromagnetic fields. Aren't photons parts of electromagnetic fields? Since I've not taken any QM yet I don't really know what a photon is. I've been told it's an electromagnetic wave. By this term I believe it sounds like a photon is an "oscillating" electromagnetic field. So if you tell me I can't consider a photon as an electromagnetic wave nor as a particle, yeah I'm confused!
What do photons share with particles? A momentum? Is it considered as a linear momentum by the way?

Photons are excited states of the electromagnetic field. The Maxwell equations describe the time evolution of the classical electromagnetic field. You can compare that to the classical equations of motion of a charged particle in a Coulomb potential. Quantize that and you get the energy levels like the energy levels of the hydrogen atom.

Now, a charged particle in orbit around some other charged particle has only 3 degrees of freedom. You need six numbers to completely specify the initial position and velocity. In a quantum description you get 3 quantum numbers (if you forget about the spin of the particle).

In case of a field, the number of degrees of freedom are infinite as you can always locally change the electromagnetic fields. This leads to an infinite number of quantum numbers that describe the energy states.

The energy is of the form:

E = (n1 + 1/2) hbar omega1 + (n2 + 1/2) hbar omega2 +...

And then we interpret n1 as being the number of photons with angular frequency omega1 etc.

Gold Member

Photons are excited states of the electromagnetic field. The Maxwell equations describe the time evolution of the classical electromagnetic field. You can compare that to the classical equations of motion of a charged particle in a Coulomb potential. Quantize that and you get the energy levels like the energy levels of the hydrogen atom.

Now, a charged particle in orbit around some other charged particle has only 3 degrees of freedom. You need six numbers to completely specify the initial position and velocity. In a quantum description you get 3 quantum numbers (if you forget about the spin of the particle).

In case of a field, the number of degrees of freedom are infinite as you can always locally change the electromagnetic fields. This leads to an infinite number of quantum numbers that describe the energy states.

The energy is of the form:

E = (n1 + 1/2) hbar omega1 + (n2 + 1/2) hbar omega2 +...

And then we interpret n1 as being the number of photons with angular frequency omega1 etc.
This seems so interesting but unfortunately over my head. Do you know any book(s) I could put my eyes in? Maybe I just have to wait for my QM course (still a year ahead) but without knowing what is a photon, I feel I don't really understand what is light.
For instance I don't know what is an "excited state of an EM field". Maybe the volume 2 of Landau & Lifgarbagez's books is good?
I didn't know photons have an angular frequency. Just curious, when we talk about the momentum of photons, does it have an equivalent in Classical Mechanics like the linear momentum or the angular momentum? I've been asked this question by a student of my class and I told her that I didn't believe so but that I was unsure. I said we talk about linear momentum of photons because they carry energy that can be transfered, like a particle with a linear momentum; but again, I said I was very unsure and that she had to ask the professor (she didn't). Now I have this doubt.

The solutions of maxwells equations in a vacuum are analogous to the solutions of minimal surface area.

A 1 dimensional electromagnetic plane wave looks a lot like a sine wave in which the electric field is perpendicular to the direction the wave is traveling (the wave velocity), and the magnetic field is perpendicular to the electric field, and the phase shift between them is 0.

This field is uniform over "planes" cut out with surface norms parallel to the velocity of the wave (i.e. the electromagnetic field vector is constant over a plane cut out over a certain time and or position).

When describing wave-particle duality, the idea original came from De Broglie, who proposed that there is a wavelength associated with a particle based on the equation

P = h/$$\lambda$$

Schroedinger then associated this wavelength with a "wave function" describing a particle.

The idea of a particle from Schroedinger's perspective is a "localized wave" whose amplitude dies out after a certain distance. However, in order to create a "localized wave," you need to add a bunch of waves together of completely different frequencies, meaning that a single particle contains many different values of momentum and energy (and since the wave is spread out over space, of position too). I think the same is true for photons, they just travel at the speed of light and have 0 rest mass.

Just curious, when we talk about the momentum of photons, does it have an equivalent in Classical Mechanics like the linear momentum or the angular momentum?

Yes, you can no doubt find a classical description of the Compton Effect which shows that photons carry a localized linear momentum and affect the trajectories of particles they collide with in a predictable way.

jtbell
Mentor

Just curious, when we talk about the momentum of photons, does it have an equivalent in Classical Mechanics like the linear momentum or the angular momentum?

Yes, classical electromagnetic fields can carry both linear and angular momentum. When you consider conservation of momentum, you have to include the momentum of both the particles and the EM fields in the system.