Construction of Schr\"odinger, Pauli and Dirac equations from Vlasov equation in case of Lorentz gauge
Abstract
On the basis of the first principle -- the law of probability conservation and the Helmholtz decomposition theorem the authors have succeeded to construct the Schr\"odinger, 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.
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