Circularly Polarized Photon, Statistical Approach and Maxwell's Equations
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint Journal |
| Terbitan: |
, 2021
|
| Subjects: | |
| Online Access: |
https://zenodo.org/record/4898325 |
Daftar Isi:
- Classically, a wave equation solution exp(ikx-iwt) follows from a tension equation for waves on a string. A similar solution Eexp(ikx-iwt) and Bexp(ikx-iwt) with E and B perpendicular follows from Maxwell’s equation for a photon (i.e. with no photons). Neither of these solutions appears to be directly linked with a statistical approach. We have argued in previous notes that exp(ipx) from a quantum free particle may be thought of as arising from statistical arguments. For example, P(x) =1 for a free particle, but P(p/x)=exp(ipx) is an option if one wishes to consider more details. This solution allows for d/dx P(p/x) = ip P(p/x).exp(ikx-iwt) leads to a Lorentz invariant argument in the exponent. For a full wavefunction W(x), P(x)=W*(x)W(x) and P(p/x) = a(p)exp(ipx)/W(x) where W(x)=Sum over p a(p)exp(ipx). For circularly polarized light moving in the z direction: E=electric field= (cos(k(t-z)), -sin(k(t-z)),0) and it seems one may link to a statistical approach because the first two components may be written as exp(-i(kx-wt)) where “i” separates the x and y component. In such a case, exp(-i(kx-wt)) represents a fixed modulus i.e. E, but there are internal cycling details i.e. E moves in a circle in the xy plane for fixed t. We argue that using ExB as a momentum density and the statistical idea of exp(-i(kx-wt)), one may postulate the wavefunction of the photon which yields two of Maxwell’s equations without sources i.e. dB/dt = -grad x E and dE/dt = grad x B.