The finding of the solution of the wave equation, formulated as the Cauchy problem, does not exhaust all possibilities of the theory. The attempt to examine that one by admitting that the time is an imaginary value is made. So the new curvilinear coordinates, named hyperbolic, are introduced in consideration. They allow for hyperbolic equations to extend a field of searching of solutions to the complex plan and give the possibility to apply powerful Fourier's method. Due to that, the wave equation takes a form of Laplace's one in polar coordinates. However, the boundary condition differs from well known Dirichlet problem that in this case looses the sence. The new condition is admitted and it is physically formulated as the description of wave from various inertial systems of coordinates. So the result is obtaining proceeding either of the momentum picture of a wave, made from the moving system of coordinates, or on the oscillogram, developed in time The analytic solution that differs from Poisson integral is deduced and gives the formulas of relativistic addition of velocities for points of wave, observing from different inertial systems. That integral was also formally yielded by using the conform translation. Additionally, in the frequencies field those formulas describe the relativistic Doppler's effect and the red shift in the wave spectrum. For oscillatory boundary condition the solution of the obtained integral gives a description of the shock waves. The fact, that some formulas of Relativity may be deduced by new way, gives the possibility to explain the relativistic theory proceeding from supposition of waving nature of quantum objects.
The entropy approach to a description of quantum processes, represented like the Markov chain, is elaborated. It is supposed that at an atomic scale the law of the conservation of entropy holds. From this principle issues the simple explanation of the different behavior of bosons and fermions in experiments with scattering particles, proved by Pauli. Introducing in consideration Markov’ chain, applied to a motion of particles, made possible to write an equation, determining the change of their states. This pure logical result, completed by physical laws, brought to a new equation, generalizing Schrödinger one. It includes electric and magnetic fields as well as the spin of particles. Analysis of its solution for a case of only electric field, led to the formula of tunnel effect. Consideration of the motion of a particle in magnetic field gave the fundamental expression of Lorentz force without any mention of electrodynamics. Addition of an angular momentum in the reasoning by including Hamiltonian, allowed deducing the result, which coincides with the spherically symmetric Schrödinger equation for hydrogen atom. In general case there is the system of equations. If the atom is put in a weak magnetic field, without a possibility of flipping, the classical formulas of Bohr radius orbits and Rydberg energy obtained. The property of intrinsic quantization of electron spin ħ/2 is explained easily as a solution of the proposed system. These equations do not repeat the known arguments only, but can predict the new phenomena. They describe the effect of spin depolarization of electrons in a strong magnetic field, earlier considered been related to vacuum polarization. The obtained solution gives its magnetic induction equal about 1012 Gs, that corresponds well with experimental data.
An attempt to bring together two different theories – classical electrodynamics and quantum mechanics is made. On the example of a hydrogen atom the problem of the hypothetic electron fall into a nucleus by means of the energy conservation law is examined. The essence of the present approach consists in the assumption, that the energy and momentum of an electron in quantum model are proportional to corresponding electromagnetic fluxes. In order to achieve the result, the new formula of momentum flux density not using Poynting vector was proposed. It states that the momentum flux depends not only on electric and magnetic components of the field, but also on a frequency of an electromagnetic wave. As the main result, it was demonstrated that the total including annihilation energy of an electron in Bohr’s atom model is equal to energy of a free electron mc2 without any mention of Relativity. An electromagnetic field inside an atom occurs quantized for each electron orbit. An additional consequence shows that the two fundamental definitions of quantum energy mc2 and ħω are interrelated. If ħω is admitted according to quantum physics, then mc2 follows automatically and vice versaю
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