Field Quantization: SHOs vs Bounded States

[yosofun]

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?

 

[marlon]

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

 

[dextercioby]

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

Daniel.

 

[hellfire]

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?

 

[Haelfix]

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.

 

[dextercioby]

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.