“Hilbert space”的概念、定义、翻译、参考文献-科学参考

Hilbert space

Physics

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. Hilbert space is named after the German mathematician David Hilbert (1862–1943), who invented the concept early in the 20th century.

Mathematics

An inner product space which is a complete metric space with respect to the norm. A Banach space is a Hilbert space if and only if the parallelogram law holds. See Riesz representation theorem.

Chemistry

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.

单词	Hilbert space
释义	Hilbert space Physics 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. Hilbert space is named after the German mathematician David Hilbert (1862–1943), who invented the concept early in the 20th century. Mathematics An inner product space which is a complete metric space with respect to the norm. A Banach space is a Hilbert space if and only if the parallelogram law holds. See Riesz representation theorem. Chemistry 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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