title: Schrödinger equation revisited.
abstract: The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton-Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave.
authors.affiliation: Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQ(ST)), Universität Ulm, D-89069 Ulm, Germany.
authors.forename: Wolfgang P
authors.initials: WP
authors.lastname: Schleich
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Greenberger
authors.forename: Donald H
authors.initials: DH
authors.lastname: Kobe
authors.forename: Marlan O
authors.initials: MO
authors.lastname: Scully
mesh_terms: D019563:Mechanics; D008962:Models, Theoretical; D011789:Quantum Theory; D013997:Time Factors