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Gavroy
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hi...does anybody know here...how you can calculate the probability density of photons?
Gavroy said:hi...does anybody know here...how you can calculate the probability density of photons?
Gavroy said:hi...does anybody know here...how you can calculate the probability density of photons?
Gavroy said:hi...does anybody know here...how you can calculate the probability density of photons?
A. Neumaier said:There is no such thing, since photons do not have a position operator.
See the entries ''Particle positions and the position operator'' and ''Localization and position operators'' in Chapter B1 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#B1
Rap said:Thanks for the link - but what would you say is being calculated by dividing the spectral energy density at some frequency by Planck's constant times that frequency?
See Secs. 3.4 and 4.1 ofGavroy said:hi...does anybody know here...how you can calculate the probability density of photons?
A. Neumaier said:It is frequency dependent, hence cannot be ''the'' number density. The only meaningful measure of the ''amount of photon stuff'' in some region S is the integral over S of the energy density.
Rap said:Yes, but for a small frequency interval df, would it not be the number density of photons with frequency f to f+df?
One shouldn't do physics like Procrustes http://en.wikipedia.org/wiki/Procrustes to match one's own preferences.Demystifier said:See Secs. 3.4 and 4.1 of
http://xxx.lanl.gov/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]
This is a very general probabilistic interpretation of relativistic many-particle states,
The paper doesn't address this (and the associated problem of gauge invariance) at all.Demystifier said:which includes photons.
A. Neumaier said:For essentially monochromatic light, you can pretend that it is by defining it in this way, but what's the use of it?
A. Neumaier said:The energy density (intensity) is very useful in optics, and sufficient without having an additional dubious concept of number density that is already meaningless for white light.
Rap said:White light has a certain energy density (U) as a function of frequency (f). Integrate U(f)/hf over all frequencies and you have the photon density.
This technical problem is easy to overcome, similarly to plane waves (momentum eigenstates) in standard QM. You can normalize it in a large but finite spacetime box, or you can use a more rigorous rigged-Hilbert-space techniques.A. Neumaier said:... interpretation as a density in space-time is incompatible with the standard Schroedinger view, since the wave function of a Schroedinger particle cannot be normalized such that the space-time integral is 1.
The paper presents a general discussion of arbitrary spin. The gauge invariance is not discussed explicitly, but it is relatively easy to do: Instead of summing over spin indices, you sum over the physical (2 for photons) polarizations.A. Neumaier said:The paper doesn't address this (and the associated problem of gauge invariance) at all.
For a useful probability interpretation one needs a representation of the wave functions as psi(x) where x is space position and momentum and angular momentum are represented in the standard way, so that |psi(x)|^2 can be viewed as a particle density, and the result is covariant under Euclidean motions.Rap said:Well, I wasn't considering "use" but I'm trying to understand the implications of there being no position operator for photons. When you say "pretend that it is", where does the pretense fail? I mean, what logical inconsistency results from assuming it is a photon density?
The probability density of photons refers to the likelihood of a photon existing in a particular state or location. It is a measure of how densely packed the photons are in a given space.
The probability density of photons is calculated by dividing the number of photons in a specific region by the total volume of that region. This gives us a measure of how likely it is to find a photon in that particular region.
Yes, the probability density of photons can affect their behavior. In regions with a high probability density, photons are more likely to interact with matter and be absorbed or scattered. In regions with a low probability density, photons are more likely to pass through without interacting.
Yes, the probability density of photons can change in different environments. For example, in a dense material like a metal, the probability density of photons will be higher compared to a vacuum. This is because the photons are more likely to interact with the material and be absorbed or scattered.
The probability density of photons can be affected by factors such as the material they are passing through, the intensity of the light source, and the wavelength of the photons. In addition, the presence of other particles in the environment can also impact the probability density of photons.