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Hilbert space

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A linear vector space that can have an infinite number of dimensions. The concept is of interest in physics because the state of a system in quantum mechanics is represented by a vector in Hilbert space. The dimension of the Hilbert space has nothing to do with the physical dimension of the system. The Hilbert space formulation of quantum mechanics was put forward by the Hungarian-born US mathematician John von Neumann (1903–57) in 1927. Other formulations of quantum mechanics, such as matrix mechanics and wave mechanics, can be deduced from the Hilbert space formulation. It is named after the German mathematician David Hilbert (1862–1943), who invented the concept early in the 20th century.

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