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Schrödinger equation as a consequence of new Vlasov type equations

Victor Valentinovich Vedenyapin, Наталия Игоревна Караваева, О А Костюк +1 more

Keldysh Institute PreprintsJan 1, 20190 citations

Connection between the weakly relativistic Vlasov and Wigner equations for various quantizations

Yu. N. Orlov, I. P. Pavlotskii

SPhDFeb 1, 19880 citations

Construction of Schrödinger, Pauli and Dirac equations from Vlasov equation in case of Lorentz gauge

E. E. Perepelkin, Б. И. Садовников, Наталья Германовна Иноземцева +1 more

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, Dirac equation, the Hamilton-Jacobi equation and the Maxwell equations. The approach described in this paper makes it possible to naturally connect the classical and quantum systems.

arXiv:2404.13580Apr 21, 20240 citations

The properties of the first equation of the Vlasov chain of equations

E. E. Perepelkin, B I Sadovnikov, N G Inozemtseva

A derivation of the first Vlasov equation as a well-known Schrödinger equation for the probabilistic description of a system and families of the classic diffusion equations and heat conduction for the deterministic description of physical systems was inferred. A physical meaning of the phase of the wave function which is a scalar potential of the probabilistic flow velocity is demonstrated. Occurrence of the velocity potential vortex component leads to the Pauli equation for one of the spinar components. A scheme for the construction of the Schrödinger equation solution from the Vlasov equation solution and vice-versa is shown. A process of introduction of the potential to the Schrödinger equation and its interpretation are given. The analysis of the potential properties gives us the Maxwell equation, the equation of the kinematic point movement, and the equation for movement of the medium within electromagnetic fields.A derivation of the first Vlasov equation as a well-known Schrödinger equation for the probabilistic description of a system and families of the classic diffusion equations and heat conduction for the deterministic description of physical systems was inferred. A physical meaning of the phase of the wave function which is a scalar potential of the probabilistic flow velocity is demonstrated. Occurrence of the velocity potential vortex component leads to the Pauli equation for one of the spinar components. A scheme for the construction of the Schrödinger equation solution from the Vlasov equation solution and vice-versa is shown. A process of introduction of the potential to the Schrödinger equation and its interpretation are given. The analysis of the potential properties gives us the Maxwell equation, the equation of the kinematic point movement, and the equation for movement of the medium within electromagnetic fields.

arXiv:1502.02062Journal of Statistical Mechanics Theory and ExperimentMay 18, 201529 citations

Derivation of Schrodinger and Dirac Equations

Spyros Efthimiades

Bulletin of the American Physical SocietyApr 18, 20050 citations

Gauge invariance and the dirac equation

Donald H. Kobe

International Journal of Theoretical PhysicsAug 1, 19828 citations

Construction of Schrödinger, Pauli and Dirac equations from Vlasov equation in case of Lorenz gauge

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Construction of Schrödinger, Pauli and Dirac equations from Vlasov equation in case of Lorenz gauge

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