DOI

The quantum state of a photon in a nanowaveguide was investigated, and it is shown that under certain conditions, it is reduced to the problem of two coupled 1D quantum harmonic oscillators (QHO) with variable frequencies. An explicit expression is obtained for the wave function of a photon, which is characterized by two vibrational quantum numbers. A quantum theory of a photon for a dissipative medium has been developed taking into account the processes of absorption and emission of photons. The mathematical expectation (ME) of the photon wave function is constructed as the product of two 2D integral representations in which the integrand is the solution of a system of two coupled second-order PDEs. The ME of the probability amplitude of the transition of a single-photon state into one of the two-photon entangled Bell states is constructed. Finally, it was proven that, in addition to frequency, spin, momentum and polarization, the photon also has a spatial structure responsible for the cross sections of processes in which this massless fundamental particle participates.
Translated title of the contributionКвантовая теория одиночного фотона в произвольной среде
Original languageEnglish
Article number58
Number of pages44
JournalParticles
Volume9
Issue number2
DOIs
StatePublished - 18 May 2026

    Research areas

  • 2D Fokker–Planck equation, Bell states, Klein–Gordon–Fock equation, Langevin–Schrödinger equation, Yang–Mills equations for Abelian fields, functional integral representation, mathematical expectation of the wave function, negentropy, non-Hermitian quantum mechanics, non-commutative geometry, open quantum system, quantum entropy, small quantized environment

    Scopus subject areas

  • Physics and Astronomy(all)
  • Mathematics(all)

ID: 155021585