Photons - Wavelength and Wavepackets

[Usaf Moji]

Hi, forgive me if this sound noobish...

For photons, I've been struggling with the interrelationship between Maxwell waves and Schrödinger waves, and further, as to the relationship between the wavelength of light and the "wavelength" of the Gaussian envelopes of wave packets.

(I guess this is only for those who accept that photons can be described using Schrödinger's equation(s) and the idea of wave packets - yeah, I saw that wikipedia note that says otherwise.)

In textbooks, a light wave is often depicted as having little wiggles within a broader Gaussian envelope - like the way they look in this guy's notes:

http://www.phys.unsw.edu.au/~sjc/physics1/summer/q25.jpg

I understand that when we speak of the "wavelength" of light, we're referring to the wavelength of the smaller sinusoidal parts within the Gaussian envelope. And I understand that the Gaussian envelope results from summing several of these smaller sinusoidal waves of varying wavelengths (varying due to the uncertainty principle).

So my question is, is the wavelength of the larger Gaussian envelope proportional to the (mean) wavelength of the sinusoids within it? In other words, if all else were equal, would red light have longer envelopes than say blue light?

All responses appreciated.

 

[Meir Achuz]

So my question is, is the wavelength of the larger Gaussian envelope proportional to the (mean) wavelength of the sinusoids within it? In other words, if all else were equal, would red light have longer envelopes than say blue light?

The length of the envelope is unrelated to the wave length of the light, unless you go to the extreme where the length of the envelope gets close to the wave length.