TY - JOUR

T1 - Quantum Theory of a Single Photon in an Arbitrary Medium

AU - Геворкян, Ашот Сережаевич

AU - Богданов, Александр Владимирович

AU - Мареев, Владимир Владимирович

PY - 2026/5/18

Y1 - 2026/5/18

N2 - 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.

AB - 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.

KW - Yang–Mills equations for Abelian fields

KW - Klein–Gordon–Fock equation; open quantum system

KW - Langevin–Schrödinger equation

KW - 2D Fokker–Planck equation

KW - Bell states

KW - Klein–Gordon–Fock equation

KW - Langevin–Schrödinger equation

KW - Yang–Mills equations for Abelian fields

KW - functional integral representation

KW - mathematical expectation of the wave function

KW - negentropy

KW - non-Hermitian quantum mechanics

KW - non-commutative geometry

KW - open quantum system

KW - quantum entropy

KW - small quantized environment

UR - https://www.mendeley.com/catalogue/555d97d1-c532-3201-a7c4-ee20284ccded/

U2 - 10.3390/particles9020058

DO - 10.3390/particles9020058

M3 - Article

VL - 9

JO - Particles

JF - Particles

SN - 2571-712X

IS - 2

M1 - 58

ER -