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Titlebook: Stochastic Processes in Quantum Physics; Masao Nagasawa Book 2000 Springer Basel AG 2000 Brownian motion.EFE.Lévy process.Markov property.

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发表于 2025-3-21 17:03:39 | 显示全部楼层 |阅读模式
书目名称Stochastic Processes in Quantum Physics
编辑Masao Nagasawa
视频video
丛书名称Monographs in Mathematics
图书封面Titlebook: Stochastic Processes in Quantum Physics;  Masao Nagasawa Book 2000 Springer Basel AG 2000 Brownian motion.EFE.Lévy process.Markov property.
描述"Stochastic Processes in Quantum Physics" addresses the question ‘What is the mathematics needed for describing the movement of quantum particles‘, and shows that it is the theory of stochastic (in particular Markov) processes and that a relativistic quantum particle has pure-jump sample paths while sample paths of a non-relativistic quantum particle are continuous. Together with known techniques, some new stochastic methods are applied in solving the equation of motion and the equation of dynamics of relativistic quantum particles. The problem of the origin of universes is discussed as an application of the theory. The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level, and some selected chapters can be used as (sub-)textbooks for advanced courses on stochastic processes, quantum theory and theoretical chemistry.
出版日期Book 2000
关键词Brownian motion; EFE; Lévy process; Markov property; Poisson process; Random Walk; Stochastic processes; di
版次1
doihttps://doi.org/10.1007/978-3-0348-8383-2
isbn_softcover978-3-0348-9543-9
isbn_ebook978-3-0348-8383-2Series ISSN 1017-0480 Series E-ISSN 2296-4886
issn_series 1017-0480
copyrightSpringer Basel AG 2000
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978-3-0348-9543-9Springer Basel AG 2000
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Stochastic Processes in Quantum Physics978-3-0348-8383-2Series ISSN 1017-0480 Series E-ISSN 2296-4886
发表于 2025-3-22 12:14:34 | 显示全部楼层
Creation and Killing of Particles,We have so far not treated “creation and killing” of Markov (diffusion) processes properly. We analyze mathematical structures of the creation and killing of Markov processes in the framework of the theory of branching Markov (diffusion) processes. Section 15.1 is of introductory nature.
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Time Reversal and Duality,-homogeneous Markov processes. To handle the time reversal and (space-time) duality of time-inhomogeneous Markov processes we will define the so-called space-time Markov processes, and prove the main theorems of time reversal and duality.
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,Construction of the Schrödinger Processes, solve the equation of motion (or the Schrödinger equation) and apply the transformation of Markov processes by a multiplicative functional. In the second case we employ the stochastic variational principle.
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