A solution to the Schrödinger equation completely mapped to the microlevel of the matter is obtained.The solution allows mathematically to ground the phenomenon of formation of the elementary antiparticles, emergence of the elementary particles from the vacuum at a high electric field intensity, to create a model of wave-particle duality and obtain a model of a gravitational wave.To obtain a model of antiparticles, a model of the emergence of elementary particles from a physical vacuum at a high electric field strength, a model of wave-particle duality, as well as a model of a gravitational wave, and a solution of the non-stationary Schrödinger equation is given.In order to obtain a solution to the non-stationary Schrödinger equation, the values that are in the real area are transferred to the imaginary area.This is achieved by jointly solving the equations of stochastic mechanics and the ARG function introduced by the author.A steady-state solution of the Rikkati-type equation written for imaginary dispersion is obtained.The steady-state solution of this equation at a constant value of the potential field makes it possible to obtain the models listed above.
A solution to the Schrödinger equation completely mapped to the microlevel of the matter is obtained.The solution allows mathematically to ground the phenomenon of formation of the elementary antiparticles, emergence of the elementary particles from the vacuum at a high electric field intensity, to create a model of wave-particle duality and obtain a model of a gravitational wave.To obtain a model of antiparticles, a model of the emergence of elementary particles from a physical vacuum at a high electric field strength, a model of wave-particle duality, as well as a model of a gravitational wave, and a solution of the non-stationary Schrödinger equation is given.In order to obtain a solution to the non-stationary Schrödinger equation, the values that are in the real area are transferred to the imaginary area.This is achieved by jointly solving the equations of stochastic mechanics and the ARG function introduced by the author.A steady-state solution of the Rikkati-type equation written for imaginary dispersion is obtained.The steady-state solution of this equation at a constant value of the potential field makes it possible to obtain the models listed above.
In the paper, we have given the quantum equation of the gravitational field intensity Eg (r, t) and electric field intensity E (r, t) for the material particles, since the gravitational field intensity Eg (r, t) and electric field intensity E (r, t) is in direct proportion to the distribution function ψ (r, t) of particle spatial position (wave function), these quantum equations are natural converted into the Schrodinger equation. In addition, we have proposed the new model about the photon and matter particles. For all particles, they are not point particles, but they have a very small volume. The photon has a vibration electric field in its very small volume. The neutral material particle, such as neutron, it has a vibration gravitational field in its very small volume. For the charge material particles, such as electron and proton, they have both vibration gravitational field and vibration electric field in their very small volume. With the model, we can explain the diffraction and interference of single slit and multiple-slit for the single photon and material particles, the volatility of all particles come from the superposition of their respective vibration field. After the vibration field of particle superposition, it shows up as a particle property. On this basis, We have obtained some new results, and realized the unification of both wave and particle and field and matter.
New insight on the principles of the quantum physics development is given. The quite different behavior of quantum microworld mechanical systems in comparison with classical mechanical macroworld systems is attributed to the drastical change of the role of the gravitation field on the dynamics of microworld mechanical systems, for which it seems to be vanishing in com- parison with the role of the gravitation field on the dynamics of macroworld mechanical systems, for which it is decisive. The conclusion on the status of the second main postulate of quantum mechanics is given. Its formulation in all textbooks has to be represented in the form of the proved statement, since the hypothesis of Schrödinger on the existence of the field scalar function, being to be observable quantity, just charge density, is strictly mathematically proved. It is shown, that the field scalar function, being to be the solution of the corresponding nonstationary in general case Schrödinger equation and being to be the function the only of coordinates and time, actually describes the state of the atomic system, more strictly its corpuscular aspect. The atomic system is considered from the positions of the field theory, that is, it is the association of elementary particles with corresponding fields. The given fields being to be the media for the particles’ propagation are responsible for the wave aspect in the characteristic of atomic systems. The wave aspect is described by the independent scalar wave-function which was also introduced in quantum physics by Schrödinger, althogh the given fact seems to be unknown to the wide circle of the readers. The second main postulate being to be mathematically strictly grounded in Schrödinger formulation of quantum nechanics, in the popular probabilistic form of quantum nechanics cannot be proved for the general case, although the probabilistic theatise, proposed by Born is true in a number of special cases, quite correctly indicated by Dirac. The possible ways of the development of quantum theory, based on clear understanding of the origin of corpuscular-wave dualism and based on the fundamental both now mathemtically grounded main postulates are analysed.
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the Schrodinger equation is proposed; the Planck constant h is expressed in terms of the characteristics of the stationary stochastic process under consideration; the probability distribution density of the n-order derivative for a n-times differentiable stationary stochastic process is determined; it is shown that the obtained generalized Schrodinger equation is applicable not only to describe the possible states of microcosm objects, but also for discrete states of a number of macrocosm stochastic systems
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions corresponding to quantum eigenstates. The constant, which determines the exponential phase volume contraction, is supposed to be a new universal constant, in addition to the speed of light and Planck constant. It is shown that statistical treatment of quantum objects as the ensembles concentrated on smooth connected attractors provides a simple explanation of stochastic behaviour of these objects as well as leads to a natural interpretation of the wave function, stationary Schrodinger equation, and scattering matrix. To validate the general hypotheses stated in the work, some physical models are presented. In particular, the models support the view that the inertial motion and quantum properties are basically determined by the vacuum as a dynamic subsystem. The matter-vacuum interaction is described formally by means of multivalued Hamilton function. A drawback of all these models is the non-locality of equations of motion stemming from the non-locality of variation of multivalued Hamilton function. This drawback can be overcome in the field theory using multivalued functionals with a local first variation opened by S. P. Novikov. Hence, a prospect of construction of the unified field theory in Einstein spirit, without a procedure of quantization is opened.
Little is known about dark matter particles save that their most important interactions with ordinary matter are gravitational and that, if they exist, they are stable, slow moving and relatively massive. Based on these assumptions, a semiclassical approximation to the Schrödinger equation under the action of a Coulomb potential should be relevant for modelling their behaviour. We investigate the semiclassical limit of the Schrödinger equation for a particle of mass M under a Coulomb potential in the context of Nelson’s stochastic mechanics. This is done using a Freidlin-Wentzell asymptotic series expansion in the parameter ϵ=ħ/M for the Nelson diffusion. It is shown that for wave functions ψ ∼ exp((R + iS)/ϵ2) where R and S are real valued, the ϵ = 0 behaviour is governed by a constrained Hamiltonian system with Hamiltonian Hr and constraint Hi = 0 where the superscripts r and i denote the real and imaginary parts of the Bohr correspondence limit of the quantum mechanical Hamiltonian, independent of Nelson’s ideas. Nelson’s stochastic mechanics is restored in dealing with the nodal surface singularities and by computing (correct to first order in ϵ) the relevant diffusion process in terms of Jacobi fields thereby revealing Kepler’s laws in a new light. The key here is that the constrained Hamiltonian system has just two solutions corresponding to the forward and backward drifts in Nelson’s stochastic mechanics. We discuss the application of this theory to modelling dark matter particles under the influence of a large gravitating point mass.