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is the time independent external with respect to the particle potential energy of the particle at each position r (see Self-action in a system of elementary particles).is the wavefunction, which is the amplitude for the particle to have a given position r at any given time t.is the particle's position in three-dimensional space,.For a single particle in three dimensions: is the reduced Planck's constant (often normalized to 1 in natural units).is the wave function, which is the probability amplitude for different configurations of the system.This section presents the equation for the general case and for the simple case encountered in many textbooks. The Schrödinger equation takes several different forms, depending on the physical situation. 2 Historical background and development.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. Schrödinger's equation can be mathematically transformed into Heisenberg's matrix mechanics, and into Feynman's path integral formulation.
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The equation is named after Erwin Schrödinger, who constructed it in 1926. Solutions to Schrödinger's equation describe not only atomic and subatomic systems, atoms and electrons, but also macroscopic systems, possibly even the whole universe. In the standard interpretation of quantum mechanics, the quantum state, also called a wavefunction or state vector, is the most complete description that can be given to a physical system. It is as central to quantum mechanics as Newton's laws are to classical mechanics.
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In physics, especially quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time. If not, you may wish to see Wikipedia's article on Schrödinger equation. If this subject is relevant to Psychology Wiki, consider creating this article. Psychology Wiki does not yet have a page about Schrödinger equation, even though this subject is highly linked to it (This is due to the initial use of content from Wikipedia).