Электронный каталог

Статья

Perepelkin, E.E.
Construction of Schridinger, Pauli and Dirac Equations from Vlasov Equation in Case of Lorenz Gauge / E.E.Perepelkin, [a.o.]. – Text : electronic // The European Physical Journal Plus. – 2025. – Vol. 140, No. 7. – P. 622. – URL: https://doi.org/10.1140/epjp/s13360-025-06547-y. – Bibliogr.: 37.

The Madelung representation for the wave function makes it possible to transform the Schrödinger equation into the Hamilton–Jacobi equation and the continuity equation (the first Vlasov equation). In the present paper, the opposite transformation is mathematically rigorously shown, that is the extended analogues of the Schrödinger and Hamilton–Jacobi equations, as well as the Pauli, Dirac, and Maxwell equations, can be obtained from the continuity equation. We have succeeded to derive an analogue of the Schrödinger equation which differs fundamentally from the well-known Schrödinger equation by the presence of “mixed” electromagnetic fields containing both the classical Maxwell fields and probabilistic fields, which are obtained by introducing a new—Lorenz gauge and the principle of self-consistency. In addition to the relation between the vector and scalar potentials for classical electromagnetic fields, the new *q -gauge provides a connection between the quantum scalar and vector potentials, which are purely statistical in nature. It is shown that if the conditions of self-consistency are met then the analogues of the Maxwell equations are valid for such new statistical “electromagnetic” fields, but with probabilistic charges and currents.



ОИЯИ = ОИЯИ (JINR)2025
Спец.(статьи,препринты) = С 133.2 - Уравнения математической физики
Бюллетени = 33/025