Schrödinger equation

In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are substantial. The equation is a mathematical formulation for studying quantum mechanical systems. It is considered a vital result in the study of quantum systems and its derivation was a significant milestone in developing the theory of quantum mechanics. It was named after Erwin Schrödinger, who derived the equation in 1925 and published it in 1926, forming the basis for his work that occasioned in his being awarded the Nobel Prize in Physics in 1933. The equation is a type of differential equation known as a wave-equation, which serves as a mathematical model of the movement of waves. The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions, as there are other quantum mechanical formulations such as matrix mechanics, introduced by Werner Heisenberg, and path integral formulation, developed chiefly by Richard Feynman. Paul Dirac incorporated matrix mechanics and the Schrödinger equation into a single formulation. Schrodingerï ½ s time-independent equation can be solved analytically for a number of simple systems. The time-dependant equation is of the first order in time but of the second order with respect to the co-ordinates, hence it is not consistent with relativity. The solutions for bound systems give three quantum numbers, corresponding to three co-ordinates, and an approximate relativistic correction is possible by including fourth spin quantum number.



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