Abstract
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.
Highlights
The evolution of the quantum mechanics is well known
The assumption of the principle of information conservation in quantum mechanics allowed proving that the operator of evolution between states in a model of Markov chain, in general case, must be expressed by matrices of complex elements that are fully correlated with a postulated definition of unitary operator
The present investigation is based on the hypothetic physical law that at an atomic scale the entropy of quantum system conserves
Summary
The evolution of the quantum mechanics is well known. In December 1900 Max Planck exposed his quantum theory of radiation. The purpose – is to obtain a generalized quantum equation for the complex wave function ψ, proceeding from a hypothetic law of conservation of entropy in Markov systems. In consequence of the real processes are irreversible, an entropy always increases according to Second law of thermodynamics This property is confined in the class of real numbers and is applying to macro systems, but do not involve complex values. What will it be in an atomic level when statistical entropy can be calculated on all states, and with an assumption, that a hypothetic law of the conservation of entropy holds? The answer to this question constitutes a purpose of the present examination
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