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04097aam a2200373 i 4500 001 B7B7C100A5B811ECBC4A196C2DECA4DB 003 SILO 005 20220317010139 008 210717t20212021sz a b 001 0 eng c 020 $a 3030626873 020 $a 9783030626877 035 $a (OCoLC)1260438686 040 $a OHX $b eng $c OHX $d IQU $d OCLCO $d OCLCF $d YDX $d BDX $d STF $d IaU $d SILO 042 $a pcc 050 4 $a QC174.17.M33 $b N34 2021 072 7 $a QA $2 lcco 072 7 $a QC $2 lcco 100 1 $a Nagasawa, Masao, $d 1933 August 1- $e author. 245 10 $a Markov processes and quantum theory / $c Masao Nagasawa. 264 1 $a Cham, Switzerland : $b BirkhaÌuser, $c [2021] 300 $a xii, 339 pages : $b illustrations ; $c 25 cm 490 1 $a Monographs in mathematics, $x 1017-0480 ; $v volume 109 520 $a This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schrödinger equation is a complex-valued evolution equation and the Schrödinger function is a complex-valued evolution function, important applications are given. 520 $a Readers will learn about new mathematical methods (theory of stochastic processes) in solving problems of quantum phenomena. Readers will also learn how to handle stochastic processes in analyzing physical phenomena.--back cover. 504 $a Includes bibliographical references (pages 321-334) and index. 505 00 $g Index. $t Branching Markov Processes with Age -- $t Smooth Motion and Random Motion -- $t On Stochastic Processes -- $t Itô's Path Analysis -- $t Equation of Motion for a Stochastic Process -- $t Kinematics of Random Motion -- $t Free Random Motion of a Particle -- $t Hooke's Force -- $t Hooke's Force and an Additional Potential -- $t Complex Evolution Functions -- $t Superposition Principle -- $t Entangled Quantum Bit -- $t Light Emission from a Silicon Semiconductor -- $t The Double-Slit Problem -- $t Double-Slit Experiment with Photons -- $t Theory of Photons -- $t Principle of Least Action -- $t Transformation of Probability Measures -- $t Schrödinger Equation and Path Equation -- $t Applications -- $t Motion induced by the Coulomb Potential -- $t Charged Particle in a Magnetic Field -- $t Aharonov-Bohm Effect -- $t Tunnel Effect -- $t Bose-Einstein Distribution -- $t Random Motion and the Light Cone -- $t Origin of the Universe -- $t Classification of Boundary Points -- $t Particle Theory of Electron Holography -- $t Escherichia coli and Meson models -- $t High-Temperature Superconductivity -- $t Momentum, Kinetic Energy, Locality -- $t Momentum and Kinetic Energy -- $t Matrix Mechanics -- $t Function Representations of Operators -- $t Expectation and Variance -- $t The Heisenberg Uncertainty Principle -- $t Kinetic Energy and Variance of Position -- $t Theory of Hidden Variables -- $t Einstein's Locality -- $t Bell's Inequality -- $t Local Spin Correlation Model -- $t Long-Lasting Controversy and Random Motion -- $t Markov Processes -- $t Time-Homogeneous Markov Proces-ses -- $t Transformations by M-Functionals -- $t Change of Time Scale -- $t Duality and Time Reversal -- $t Time Reversal, Last Occurrence Time -- $t Time Reversal, Equations of Motion -- $t Conditional Expectation -- $t Paths of Brownian Motion -- $t Applications of Relative Entropy -- $t Relative Entropy -- $t Variational Principle -- $t Exponential Family of Distributions -- $t Existence of Entrance and Exit Functions -- $t Cloud of Paths -- $t Kac's Phenomenon of Propagation of Chaos -- $t Extinction and Creation -- $t Extinction of Particles -- $t Piecing-Together Markov Processes -- $t Branching Markov Processes -- $t Construction of Branching Markov Processes -- $t Markov Processes with Age -- $t Branching Markov Processes with Age -- $g Bibliography -- $g Index. 650 0 $a Markov processes. 650 0 $a Quantum theory. 650 7 $a Markov processes. $2 fast $0 (OCoLC)fst01010347 650 7 $a Quantum theory. $2 fast $0 (OCoLC)fst01085128 830 0 $a Monographs in mathematics ; $v v. 109. $x 1017-0480 941 $a 1 952 $l OVUX522 $d 20231117011840.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=B7B7C100A5B811ECBC4A196C2DECA4DBInitiate Another SILO Locator Search