The Quantum Hamilton–Jacobi Equation and the Link Between Classical and Quantum Mechanics

We study how the classical Hamilton's principal and characteristic functions are generated from solutions of quantum Hamilton–Jacobi equation. While in classically forbidden regions these quantities directly tend to ones, this is not case allowed regions. There, limit reached only if fluctuations eliminated by means coarse-graining averages. Analogously, scheme bringing motion's equations arises a similar formal procedure.Quanta 2022; 11: 42–52.