On simulation of the photon wave function to explain the Young’s experiment and prospects for its use in quantum cryptography

Abstract

The method developed in previous works for building the photon wave function in configuration representation is briefly described. The simulation of such function (wave packet) appropriate to femtosecond laser radiation, using the distribution of Gauss of photon momenta in the state of a single laser impulse is expounded. By other appropriate simulated wave function of photon the light interference in Young’s experiment is explained within the frame of quantum mechanics without the attraction of transition probability amplitudes used in approach of quantum electrodynamics. This allows us considering interference phenomena for photons and particles from the same basis of the quantum-mechanical principle of superposition employed to the wave function built in the configuration space. Using the building apparatus of photon quantum mechanics, the Malus law postulated in quantum theory is justified. The relevance of new experiments to study the interaction of quantum objects between themselves and the physical vacuum, which would reveal the origins of the mathematical description of quantum states using the wave function of these quantum objects, is substantiated. It is suggested that the ideas of constructing the wave function of a free photon in the coordinate representation can find relevance in the field of quantum cryptography.

On numerical and approximate analytical modeling of single- and two-photon Young's experiment using the photon coordinate wave function

“…The PWF in coordinate representation, constructed and substantiated in a number of previous authors works [1,2,[18][19][20][21] on the basis of Maxwell's equations in the Majorana form [29], can be written in the form of a wave packet as an integral over the entire space of the photon wave vector…”

“…Generally speaking, the construction of the coordinate PWF, despite numerous arguments of the impossibility of its justification [3][4][5][6][7][8][9], is periodically discussed, and its various variants are proposed [10][11][12][13][14][15][16][17]. In this article we will rely in the first approach, on our [1,2,[18][19][20][21] method of its constructionwithin the framework of photon quantum mechanicsin the form of a 6-component wave packet, which is the superposition (integral) of generalized eigenfunctions of the operators of momentum, energy, and helicity of photon in the bivector representation. This method does not use the second quantization, but is, in fact, the result of the "primary" quantization of the classical electromagnetic field.…”

“…. In ( 2) and ( 3), the complex polarization vectors ) ( e 1 k  satisfy a number of orthonormal relations [1,2,[18][19][20][21] and are generally written as follows: , generally speaking, can be set arbitrarily (or calculated), but they must also satisfy the orthonormality condition, which can be combined into a chain of general relations, taking into account (6)…”

“…which realize a propagating spherical wave corresponding to the state of a photon with zero average momentum and its mean modulus 0 k  . The choice of (9) forms a delta-like function, which allows one to single out a monochromatic wave in the decomposition (1) in terms of plane waves, and also gives a fairly simple analytical formula for the photon wave function [21,32]. The main ideas according to [21] of this derivation are as follows.…”

“…The choice of (9) forms a delta-like function, which allows one to single out a monochromatic wave in the decomposition (1) in terms of plane waves, and also gives a fairly simple analytical formula for the photon wave function [21,32]. The main ideas according to [21] of this derivation are as follows. Let r  and r  define the radius vector r in the spherical coordinate system of the configuration space.…”