Structure of the Schrödinger Dynamics: Rediscovery of Quantum Mechanics

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 fundament