Structure of the Schrödinger Dynamics
Rediscovery of Quantum Mechanics
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Beschreibung
This book aims to transcend both the extraordinary success of quantum theory founded upon the Schrödinger equation and the long-standing confusion surrounding its “interpretation,” in order to reveal the structure of a new era of quantum theory. The book develops its central ideas through three pillars. First, the Schrödinger equation is derived from first scratch, thereby clarifying the physical meaning of the wave function and the equation itself. Second, a matrix-valued quantum path integral endowed with a well-defined integration measure is constructed as the Green’s function of a real-valued Schrödinger equation. This framework guarantees the convergence of the Feynman path integral and, through its connection with the Feynman–Kac formula, elucidates the deep relationship between quantum theory and stochastic processes. Third, quantum stochastic differential equations are established, providing a dynamical description of individual events rather than ensembles, and offering a fundamentally new perspective on quantum phenomena. From this framework follow a variety of striking theoretical consequences: the rejection of wave-function collapse; the spontaneous resolution of entanglement responsible for ultra-long-range correlations; the dynamical origins of probabilistic behavior and uncertainty relations; the buildup of quantum canonical equations of motion and reduction to classical Hamiltonian canonical equations; the symmetry and asymmetry of time reversal; the dual relationship between quantum theory and stochastic process theory; and the mechanism underlying the formation of interference fringe patterns in the double-slit experiment, and so on. This book is intended for graduate students and researchers who have completed a standard course in quantum mechanics through texts such as Dirac’s, as well as for scientists working in quantum science—especially quantum physics and measurement, quantum chemistry, quantum biology, quantum technology, quantum information theory, and the study of single-event quantum dynamics. It will also serve as a valuable reference for researchers concerned with the foundations and interpretations of quantum theory.
This book aims to transcend both the extraordinary success of quantum theory founded upon the Schrödinger equation and the long-standing confusion surrounding its “interpretation,” in order to reveal the structure of a new era of quantum theory. The book develops its central ideas through three pillars. First, the Schrödinger equation is derived from first scratch, thereby clarifying the physical meaning of the wave function and the equation itself. Second, a matrix-valued quantum path integral endowed with a well-defined integration measure is constructed as the Green’s function of a real-valued Schrödinger equation. This framework guarantees the convergence of the Feynman path integral and, through its connection with the Feynman–Kac formula, elucidates the deep relationship between quantum theory and stochastic processes. Third, quantum stochastic differential equations are established, providing a dynamical description of individual events rather than ensembles, and offering a fundamentally new perspective on quantum phenomena. From this framework follow a variety of striking theoretical consequences: the rejection of wave-function collapse; the spontaneous resolution of entanglement responsible for ultra-long-range correlations; the dynamical origins of probabilistic behavior and uncertainty relations; the buildup of quantum canonical equations of motion and reduction to classical Hamiltonian canonical equations; the symmetry and asymmetry of time reversal; the dual relationship between quantum theory and stochastic process theory; and the mechanism underlying the formation of interference fringe patterns in the double-slit experiment, and so on. This book is intended for graduate students and researchers who have completed a standard course in quantum mechanics through texts such as Dirac’s, as well as for scientists working in quantum science—especially quantum physics and measurement, quantum chemistry, quantum biology, quantum technology, quantum information theory, and the study of single-event quantum dynamics. It will also serve as a valuable reference for researchers concerned with the foundations and interpretations of quantum theory.
Explores quantum phenomena beyond the Schrödinger equation alone Develops three pillars of quantum dynamics beyond the Schrödinger equation Offers a rediscovery of quantum dynamics
Autor*in
Kazuo Takatsuka
Themen in »Structure of the Schrödinger Dynamics«
Derivation of real-valued Schrödinger equation from scratch Wiener measure for the real-valued quantum path integrals Stochastic differential equations for quantum paths Three pillars of quantum dynamics to build the interpretation on Spontaneous disentanglement to ease Einstein’s worry Disentanglement and Bell’s inequality Physical meaning of the Schrödinger vector (wavefunction) No collapse of wavefunction Mechanical role of the Schrödinger equation Mechanical origin of the Born probability interpretation Dynamical origin of uncertainty relations Origin of the fringe patterns in the double-slit experiment Unitarity and semi-group property in time-propagation Quantum mechanical canonical equations and classical mechanics