# Interpretation of Light Beam Intensity in QM

1. Oct 11, 2011

### Jilvin

I am starting to become confused when reading about quantum mechanics and its treatment of photons. I heard somewhere (I can't recall where) that the characteristic intensity of a photon beam was give by I = E/$\omega$, where $\omega$ is the angular frequency of the beam. However, I can't seem to reconcile this with the fact that, since the energy of a photon is given in quantum mechanics as E = $\hbar$$\omega$, that the intensity I would simply reduce to $\hbar$ in every single case.

This doesn't seem correct at all, as the entire study of squeezed coherent states of light is apparently based upon studies of light beams with high differences between phase angle uncertainty and intensity uncertainty....

What am I interpreting incorrectly?

2. Oct 12, 2011

### Jilvin

Nevermind, I think I've got it now. The intensity uncertainty is only valid for *large* photon numbers. Here's what I mean. In the study of squeezed light, the uncertainty ΔIΔη≥$\hbar$/2 is important (where I is the intensity and η is the phase). I couldn't comprehend just what ΔI (indeterminacy in intensity) meant because if characteristic intensity is given by I=E/ω; and for any *single* photon the energy E is given by $\hbar$ω, then it would appear that ΔI = 0 because it would always equal $\hbar$. However, I didn't consider that the above uncertainty principle was for large photon numbers, so that the intensity given by N$\hbar$ for N photons would be uncertain in the *number of photons* emitted in the beam.

Thus, the only possibility for ΔI making any sense as a quantity was if the photon quantity varied between measurement. I did some checking, and this is indeed the case. You can close this post now.