23 citations · 133 across the 30 of their papers we have counts for
30 papers
Kinematic properties of the Pauli equation
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
Based on the Wigner-Vlasov formalism, this paper investigates the kinematic properties of the Pauli equation. It is shown that the probability current associated with the Pauli equ…
The Maxwell class exact solutions to the Schrödinger equation and continuum mechanics models
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
By applying the nonlinear Legendre transform to the continuity equation, this paper derives exact solutions to the Schrödinger equation and the equations of continuum mechanics. A…
Exact solutions for the relativistic dynamics of a self-consistent system with electromagnetic and gravitational interaction within the Wigner-Vlasov formalism
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitation…
New exact solutions of the 3D Schrödinger equation
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
Previously we found a unique quantum system with a positive gauge-invariant Weyl-Stratonovich quasi-probability density function which can be defined by the so-called «quadratic fu…
Construction of Schrödinger, Pauli and Dirac equations from Vlasov equation in case of Lorentz gauge
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
On the basis of the first principle -- the law of probability conservation and the Helmholtz decomposition theorem the authors have succeeded to construct the Schrödinger, Pauli, D…
Investigation of the dynamics of transverse oscillations of a vertical rod under gravity, friction, and thermal expansion
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
The paper considers the mathematical formulation of the problem of transverse oscillations of a vertical rod under gravity, friction and external pulse effect, leading to thermal e…
Wigner function properties for electromagnetic systems
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
Using the Wigner-Vlasov formalism, an exact 3D solution of the Schrödinger equation for a scalar particle in an electromagnetic field is constructed. Electric and magnetic fields a…
Is the Moyal equation for the Wigner function a quantum analogue of the Liouville equation?
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +2
The Moyal equation describes the evolution of the Wigner function of a quantum system in the phase space. The right-hand side of the equation contains an infinite series with coeff…
PSI-Moyal equation
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
A full consideration of classical and quantum systems with radiation (electromagnetic/gravitational) requires the involvement of a mathematical description in the generalized phase…
Dispersion chain of quantum mechanics equations
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
Based on the dispersion chain of the Vlasov equations, the paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The propose…
PSI-Vlasov equation
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
A new equation for describing physical systems with radiation is obtained in this paper. Examples of such systems can be found in plasma physics, accelerator physics (synchrotron r…
Exact time-dependent solution of the Schrödinger equation, its generalization to the phase space and relation to the Gibbs distribution
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to appro…
The Wigner function negative value domains and energy function poles of the polynomial oscillator
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +2
For a quantum oscillator with the polynomial potential an explicit expression that describes the energy distribution as a coordinate (and momentum) function is obtained. The presen…
Dispersion chain of Vlasov equations
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In…
The Wigner function negative value domains and energy function poles of the harmonic oscillator
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
For a quantum harmonic oscillator an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is s…
Extended Wigner function for the harmonic oscillator in the phase space
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wa…
Universal density matrix for the phase space
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
In this paper, a new representation of the Wigner function for a quantum system in the phase space is proposed. The new representation is of the form $W=\operatorname{Sp}\left[ ρ\m…
The Vlasov equation correct application based on the higher orders kinematic values for the dissipative systems description
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
This paper revises traditional phenomenological approaches to the application of Vlasov equation to describe the dissipative systems. The original equation by A.A. Vlasov obtained…
A new class of exact solutions of the Schrodinger equation
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva +1
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, usi…
The chain of quantum mechanics equations
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva
The chain of quantum mechanics equations is constructed for wave functions depending on coordinate and time as well as on velocity, acceleration and acceleration of higher orders.
Dissipative systems entropy
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva
In this paper, we introduce the generalized phase space , which expands the known phase space $\left( \vec{r},\vec{…
The new modified Vlasov equation for the systems with dissipative processes
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva
A new modified Vlasov equation has been obtained in this paper for the systems with dissipative phenomena such as, for example, plasma with irradiation.
- model of micro- and macrosystems
E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva
A mathematical model (referred as - model for convenience) has been developed, which allows describing certain class of micro- and macrosystems. - model is based on continu…
Riemann surface and quantization
E. E. Perepelkin, B. I Sadovnikov, N. G. Inozemtseva
This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization…