Skip to Main content Skip to Navigation
New interface
Journal articles

Quantized Vector Potential and the Photon Wave-function

Abstract : The vector potential function ${\overrightarrow{\alpha }}_{k\lambda }(\overrightarrow{r},t)$ for a k-mode and λ-polarization photon, with the quantized amplitude α 0k (ω k ) = ξω k , satisfies the classical wave propagation equation as well as the Schrodinger's equation with the relativistic massless Hamiltonian $\mathop{H}\limits^{\sim }=-i\hslash c\overrightarrow{\nabla }$ and finally an equivalent quantum equation for the vector potential amplitude operator ${\mathop{\alpha }\limits^{\sim }}_{0}=-i\xi c\overrightarrow{\nabla }$. Thus, ${\overrightarrow{\alpha }}_{k\lambda }(\overrightarrow{r},t)$ behaves as a wave function for the photon within a non-local representation that can be suitably normalized. It is deduced that the probability for detecting a k-mode photon around a point on the propagation axis depends on the square of the angular frequency. Taking into account the left and right circularly polarized states and weighting ${\overrightarrow{\alpha }}_{k\lambda }(\overrightarrow{r},t)$ by ${\omega }_{k}\sqrt{2{\varepsilon }_{0}}$ we define a six components function as a general function for a k-mode photon. The square of the modulus of the defined general function gives the energy density at a given coordinate which depends on the fourth power of the angular frequency. The amplitudes of the electric and magnetic fields of a single k-mode photon free of cavity are also calculated and it is shown that they are proportional to the square of the angular frequency. In this way, the influence of the photon electric and/or magnetic fields on the energy levels of atoms and molecules might be used for a non-destructive photon detection.
Document type :
Journal articles
Complete list of metadata

Cited literature [7 references]  Display  Hide  Download
Contributor : Catherine Cardon Connect in order to contact the contributor
Submitted on : Friday, January 26, 2018 - 3:07:36 PM
Last modification on : Friday, October 14, 2022 - 9:10:00 AM
Long-term archiving on: : Friday, May 25, 2018 - 8:52:03 AM


Publisher files allowed on an open archive



Constantin Meis, Pierre-Richard Dahoo. Quantized Vector Potential and the Photon Wave-function. Journal of Physics: Conference Series, 2017, 6th International Conference on Mathematical Modelling in Physical Sciences (IC-MSQUARE 2017), 28–31 August 2017, Pafos, Cyprus, 936 (1), pp.012004. ⟨10.1088/1742-6596/936/1/012004⟩. ⟨insu-01576537⟩



Record views


Files downloads