Schrödinger equation
Sign in to savepartial differential equation describing how the quantum state of a non-relativistic physical system changes with time
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The Schrödinger equation is a mathematical formula that describes how particles behave and change over time at the quantum scale, the world of atoms and subatomic particles. It's one of the foundation stones of quantum mechanics because it allows scientists to predict the properties and behavior of matter at its smallest scales.
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The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.
Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equation predicted bound states of the atom in agreement with experimental observations.