Photon position eigenstates in configuration space

Abstract:The expressions of the eigenfunctions of the Hawton photon position operator in configuration space are derived for several classes of wave function, including the Riemann--Silberstein and Landau--Peierls cases. Although these eigenfunctions have a simple form in momentum space, the explicit characterization of their representations in configuration space is rather more involved. We provide closed expressions of these eigenfunctions in terms of linear combinations of the complete elliptic integrals $K(\kappa)$ and $E(\kappa)$ with modulus $\kappa$ depending on trigonometric functions of the polar angle. We show that they diverge not only at the value $\mathbf q$ of the position eigenvalue, but also on a plane containing $\mathbf q$ and that they decay as inverse powers of the distance from $\mathbf q$.

17 pages, 2 figures. Minor changes from previous version to match the published paper

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optics (physics.optics)

arXiv:2605.25857 [quant-ph]

(or arXiv:2605.25857v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.25857 Focus to learn more arXiv-issued DOI via DataCite

Phys.Rev. A 114 (2026) 022204

https://doi.org/10.1103/ll57-rj9l Focus to learn more DOI(s) linking to related resources

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