Field Quantization: SHOs vs Bounded States

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    Field Quantization
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Discussion Overview

The discussion revolves around the quantization of the electric field, specifically comparing the treatment of photons as simple harmonic oscillators versus their potential representation as bound states in an infinite square well. Participants explore the physical interpretations and implications of these different models within the context of quantum field theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the physical interpretation and justification of using simple harmonic oscillator operators for field quantization, suggesting an alternative model of bound states in an infinite square well.
  • Another participant asserts that photons do not behave like simple harmonic oscillators, emphasizing their unique properties as photons.
  • A different viewpoint discusses the derivation of harmonic oscillator behavior from the Fourier expansion of the electromagnetic potential, questioning how one could propose a different behavior for the field amplitudes.
  • One participant reflects on the fundamental nature of the harmonic oscillator in physics, suggesting its relevance across various branches and its role in linearized perturbation theory.
  • A later reply recommends reading about axiomatic field theory to clarify the concept of quantizing classical systems.

Areas of Agreement / Disagreement

Participants express differing views on whether photons can be accurately modeled as simple harmonic oscillators or if alternative models are more appropriate. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

The discussion highlights the complexity of field quantization and the assumptions underlying different models, such as the harmonic oscillator and bound states. There is an acknowledgment of the need for careful consideration of boundary conditions and system specifics.

yosofun
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i have read through a mathematical description of the quantization of the electric field through the simple harmonic oscillator raising/lowering operators. what is the physical interpretation and justification for this?

what if one assumes that photons do not behave like simple harmonic oscillators... but (perhaps) say bound states in an infinite square well. how would this change field quantization?
 
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yosofun said:
i have read through a mathematical description of the quantization of the electric field through the simple harmonic oscillator raising/lowering operators. what is the physical interpretation and justification for this?
what if one assumes that photons do not behave like simple harmonic oscillators... but (perhaps) say bound states in an infinite square well. how would this change field quantization?

What you are asking about is the advent of Second Quantization or Canonical quantization. Since i am too lazy to write all of this down, i suggest you first do some reading and let us then elaborate further.

marlon
 
Photons do not behave like simple harmonic oscillators, they behave like photons :

Daniel.
 
yosofun said:
i have read through a mathematical description of the quantization of the electric field through the simple harmonic oscillator raising/lowering operators. what is the physical interpretation and justification for this?
what if one assumes that photons do not behave like simple harmonic oscillators... but (perhaps) say bound states in an infinite square well. how would this change field quantization?
When you expand the electromagnetic potential A in a Fourier series and insert this in the wave equation for A, you obtain that the field amplitudes behave like a harmonic oscilator. How could you get or postulate a different behaviour?
 
Well, I like to think of it as this: The harmonic oscillator is sort of the first defacto thing to think about in any branch of physics , its use is more or less fundamental whether it classical mechanics, quantum mechanics or field theory.

Physical systems that are tractable must have some semi or quasi stable equilibrium point in some set of variables, and small fluctuations away from this are guarenteed to have harmonic behaviour. So its natural, when you are trying to construct a linearized perturbation theory, to write out what you know and expect for the harmonic oscillator in such a situation, and then expand it out and work with that (being careful to match things appropriately along with all the information of the system, boundary conditions etc).

A famous colleague once said physics was 90% solved by Fourier analysis, the rest is just nitty gritty details =)

A tiny bit oversimplified, but morally kinda true.
 
On a serious note now, i'd say a good book on axiomatical field theory should get you clear with what "quantizing a classical system" means.

Daniel.
 

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