Saturday, September 5, 2009

Schrödinger Equation

The Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time. It is as central to quantum mechanics as Newton's laws are to classical mechanics. The Schrödinger equation can be mathematically transformed into Heisenberg's matrix mechanics, and into Feynman's path integral formulation. The Schrödinger equation describes time in a way that is inconvenient for relativistic theories, a problem which is not as severe in Heisenberg's formulation and completely absent in the path integral.

In the standard interpretation of quantum mechanics, the quantum state is the most complete description which can be given to a physical system. Solutions to Schrödinger's equation describe not only atomic and subatomic systems, atoms and electrons, but also macroscopic systems, possibly even the whole universe. The equation is named after Erwin Schrödinger, who constructed it in 1926.

The Schrödinger equation describes the behaviour of an electron of energy E in a potential V in terms of the wave function y. The time-independent, one-dimensional form of the equation is: d2y/dx2 + (8p2m/h2)[E - V]y = 0 where m is the electron mass and h is Planck's constant.