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The exact nature of this Hilbert space is dependent on the system; for example, the position and momentum states for a single non-relativistic spin zero particle is the space of all square-integrable functions, while the states for the spin of a single proton are unit elements of the two-dimensional complex Hilbert space of spinors.
Canonically cited as Dunford and Schwartz, [1] the textbook has been referred to as "the definitive work" on linear operators. [2]: 2 The work began as a written set of solutions to the problems for Dunford's graduate course in linear operators at Yale. [3]: 30 [1] Schwartz, a prodigy, had taken his undergraduate degree at Yale in 1948, age 18 ...
Geometry and the Imagination is the English translation of the 1932 book Anschauliche Geometrie by David Hilbert and Stefan Cohn-Vossen. [1] The book was based on a series of lectures Hilbert made in the winter of 1920–21. The book is an attempt to present some then-current mathematical thought to "contribute to a more just appreciation of ...
The term Hilbert geometry may refer to several things named after David Hilbert: . Hilbert's axioms, a modern axiomatization of Euclidean geometry; Hilbert space, a space in many ways resembling a Euclidean space, but in important instances infinite-dimensional
Every inner product space is also a normed space. A normed space underlies an inner product space if and only if it satisfies the parallelogram law, or equivalently, if its unit ball is an ellipsoid. Angles between vectors are defined in inner product spaces. A Hilbert space is defined as a complete inner product space. (Some authors insist ...
That is called Hilbert space (introduced by mathematicians David Hilbert (1862–1943), Erhard Schmidt (1876–1959) and Frigyes Riesz (1880–1956) in search of generalization of Euclidean space and study of integral equations), and rigorously defined within the axiomatic modern version by John von Neumann in his celebrated book Mathematical ...
One who had to leave Germany, Paul Bernays, had collaborated with Hilbert in mathematical logic, and co-authored with him the important book Grundlagen der Mathematik [22] (which eventually appeared in two volumes, in 1934 and 1939). This was a sequel to the Hilbert–Ackermann book Principles of Mathematical Logic from 1928.
The Fock space is the (Hilbert) direct sum of tensor products of copies of a single-particle Hilbert space () = = = (()) (())Here , the complex scalars, consists of the states corresponding to no particles, the states of one particle, () the states of two identical particles etc.