Quantization Explained: Understanding Photon Energy Packages

[I'mnotarobot]

Hi, I'm having a hard time understanding what exactly it means to be quantized.
I know that electromagnetic radiation is quantized, and that means coming in little "packages" of energy, I can't really wrap my head around this, and would like if someone could explain this a better way maybe?

Would this then apply that photons are essentially these "packages" of energy?

Thanks

 

[bhobba]

Hi, I'm having a hard time understanding what exactly it means to be quantized.

Yes they do come in packets of energy.

Why? Well, basically its what our theories predict.

There is a deep mathematical reason that can't be explained in words, and these lectures give the detail:


Unfortunately the question you have asked is very very deep and can't be explained in lay terms. Even using math its quite cutting edge requiring advanced concepts such as Pade approximations:
https://en.wikipedia.org/wiki/Padé_approximant

Thanks
Bill

 

[strangerep]

I'm having a hard time understanding what exactly it means to be quantized. I know that electromagnetic radiation is quantized, and that means coming in little "packages" of energy,

Since you've given this thread an "I" tag, I'll say that the above is not really what "quantization" means, in general.

A better way to get the meaning is as follows. In classical mechanics, we have various dynamical variables expressed as functions on phase space. A particular (class of) systems is characterized by the Lie algebra formed among the dynamical variables using Poisson brackets. Quantization is then the procedure of representing this same Lie algebra as operators on a Hilbert space. This deceptively simple step has stunningly far-reaching consequences.

(Sorry if this answer is at the wrong level. If you haven't yet studied Hamiltonian mechanics and Poisson brackets, this won't make much sense.)

 

[I'mnotarobot]

Interesting, I have studied Hamiltonian mechanics a bit, as in I do know how to apply hamiltonian dynamics for the equation of motion. However, some of the derivations at the time were a bit hard to follow and the terms here I do recognize but it seems we never went to deep into it. Thank you for your reply, I feel I will be understanding exactly what you said very soon, and it seems to be a bit more complex as I hoped. That's ok though, I'm very fascinated by your reply, gives me something to look into! Thanks!

Thank you @strangerep and @bhobba

 

[A. Neumaier]

photons are essentially these "packages" of energy?

Yes. This is by far the best way to understand photons in experiments, although one has to be a bit careful since there are two slightly different uses of the word photon. See http://arnold-neumaier.at/ms/lightslides.pdf

 

[I'mnotarobot]

Thank you!

 

[A. Neumaier]

Thank you!

Since you have seen Hamiltonian mechanics, you can probably understand large parts of my book mentioned in https://www.physicsforums.com/posts/5335466/