In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.
In classical mechanics Newton's second law, (F = ma), is used to mathematically predict what a given system will do at any time after a known initial condition. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function (also called a "state function").:1–2
The concept of a wavefunction is a fundamental postulate of quantum mechanics. Although Schrödinger's equation is often presented as a separate postulate, some authors:Chapter 3 show that some properties resulting from Schrödinger's equation may be deduced just from symmetry principles alone, for example the commutation relations. Generally, "derivations" of the Schrödinger equation demonstrate its mathematical plausibility for describing wave–particle duality, but to date there are no universally accepted derivations of Schrödinger's...