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Deduction of the Klein–Fock–Gordon equation from a non‐Markovian stochastic equation for real pure‐jump process
Author(s) -
Skorobogatov G. A.
Publication year - 2002
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10212
Subject(s) - fock space , jump , markov process , master equation , mathematics , jump process , mathematical physics , physics , quantum mechanics , quantum , statistics
From the Madelung's work in 1926, it became clear that the pair of adjoint Schrödinger equations is equivalent to two equations of hydrodynamic representation for probability density and mean momentum Both these equations can be derived from the quantum transport equation (QTE) for a probability density P (, , t) as two equations for the two first moments Then, QTE can be obtained from a non‐Markovian stochastic Kolmogorov–Gikhman–Skorokhod equation for a real pure‐jump process. Similarly, the Klein–Fock–Gordon equation follows from non‐Markovian relativistic QTE (RQTE). Thus, all quantum mechanics as mathematical theory is a topic of the theory of real pure‐jump non‐Markovian stochastic processes. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002