# Classical limit of Quantum Optics

1. Apr 19, 2010

### Xian

I don't profess of a knowledge of QED, and am in fact incredibly ignorant of its formulation and nuances, however I do understand that its never been refuted and is the crown jewel of physical models. So I will take it as fact for this post.

What confuses me, is that in quantum mechanics, every particle must be described by a wavefunction which is a complete characterization of its state. So it follows that a photon has a wavefunction.

Classically, when we observe light, we are told that we measure an undulatory wave packet of some local frequency ω. When we look at the Fourier transform of the wave packet we get peaks at the frequencies ω and -ω and the rest of the constituent frequencies clump around it (due to the fact that bounded wave packets must be built from a continuum of waves).

If this is indeed what is measured, how do the photon wavefunctions combine to create such an elegant waveform?
What does a photon wave function look like?
And where do E-fields and B-fields come in for the single photon case?

2. Apr 19, 2010

### jeblack3

In QED it works the other way around. You start from the electromagnetic field. Then you treat waves of each wavelength as independent harmonic oscillators. By applying quantum mechanics, we find that each oscillator has a discrete set of energy states, and the difference between any two consecutive energy levels is Planck's constant times the frequency of light at that wavelength. When one of the oscillators is in the first energy level above its ground state, that means there is one photon.

3. Apr 21, 2010

### Xian

Hmm, so in essence QED quantizes the field? And when this quantization is done, we identify excited states with photons?

A related question then is what do the photon wavefunctions look like?