Initial mathematical modeling of photon radiation in fiber optic networks of various types

The article provides mathematical modeling of the transfer process in a cylindrical fiber-optic tube of a monochromatic light beam. To describe the phenomenon, the approach of gradually increasing the mathematical accuracy and complexity of the problem is used. The initial stage is a dual mathematical formalism for the Schrodinger equation with separate forms of the Hamiltonian for the Laplace and Nabla operators. A partial comparison with the formalism of Maxwell's equations and a complete mathematical visualization of the set of solutions for each of the tuples of solutions of the psi function are given. Interesting features of this approach are revealed, with the definition of some unexpected formulations that take into account the role of quantum mechanical phenomena in the process of mathematical modeling and investigation of photon beams in fiber-optic networks. The conclusion was to determine the necessity and relevance of the topic of further expansion of the study in the direction of considering the process within the framework of the formalism of increased accuracy through the Pauli, Klein-Gordon, Dirac equations, the Riemann-Silberstein formalism in an expanded topological space.