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Rigged Hilbert space information


In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis. Such spaces were introduced to study spectral theory in the broad sense.[vague] They bring together the 'bound state' (eigenvector) and 'continuous spectrum', in one place.

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Rigged Hilbert space

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of rigged Hilbert space places this idea in an abstract functional-analytic framework. Formally, a rigged Hilbert space consists of a Hilbert space H,...

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Hilbert space

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In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)...

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Dirac delta function

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allowing distributions as well, i.e., to replace the Hilbert space with a rigged Hilbert space. In this context, the position operator has a complete...

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List of functional analysis topics

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Reproducing kernel Hilbert space Riesz representation theorem Rigged Hilbert space Spectral theorem, Spectral theory Trace class Normed vector space Unit ball...

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List of things named after David Hilbert

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reciprocity Hilbert scheme Hilbert space Hilbert dimension Projective Hilbert space Reproducing kernel Hilbert space Rigged Hilbert space Semi-Hilbert space Hilbert...

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Weak topology

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topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used for the...

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Nuclear space

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properties. Nuclear spaces are however quite different from Hilbert spaces, another generalization of finite-dimensional Euclidean spaces. They were introduced...

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Observable

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ISBN 978-3-527-34553-3. de la Madrid Modino, R. (2001). Quantum mechanics in rigged Hilbert space language (PhD thesis). Universidad de Valladolid. Teschl, G. (2014)...

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Spectral theorem

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Other link de la Madrid Modino, R. (2001). Quantum mechanics in rigged Hilbert space language (PhD thesis). Universidad de Valladolid. M. Reed and B....

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Probability amplitude

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clearly do not belong to L2(X). By replacing the state space by a suitable rigged Hilbert space, however, the rigorous notion of eigenstates from spectral...

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Quantum decoherence

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continuous and discrete indexes, in which case we would have to use a rigged Hilbert space and be more careful about what we mean by orthonormal, but that's...

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Generalized function

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Beppo-Levi space Dirac delta function Generalized eigenfunction Distribution (mathematics) Hyperfunction Laplacian of the indicator Rigged Hilbert space Limit...

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Schwartz kernel theorem

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defined on two topological vector spacesPages displaying wikidata descriptions as a fallback Rigged Hilbert space – Construction linking the study of...

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Mathematical formulation of quantum mechanics

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uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms...

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Representation theory of the Galilean group

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these energy-momentum eigenvalues. (This subspace only exists in a rigged Hilbert space, because the momentum spectrum is continuous.) The subspace is spanned...

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Spectral theory

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deal with generalized eigenfunctions (for example, by means of a rigged Hilbert space). On the other hand, it is simple to construct a group algebra, the...

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Infraparticle

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a continuous mass spectrum and eigenstates of m only exist in a rigged Hilbert space. The electron, and other particles like it is called an infraparticle...

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Entropy as an arrow of time

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tangent space of PSL(2,R). Research on irreversibility in quantum mechanics takes several different directions. One avenue is the study of rigged Hilbert spaces...

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Volodymyr Koshmanenko

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Koshmanenko, V. Construction of singular perturbations by the method of rigged Hilbert spaces, Journal of Physics A: Mathematical and General, 38, 4999–5009 (2005)...

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Polynomial ring

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(German for "zero-locus theorem") is a theorem, first proved by David Hilbert, which extends to the multivariate case some aspects of the fundamental...

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List of abstract algebra topics

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Gaussian integer Theorems and applications Algebraic geometry Hilbert's Nullstellensatz Hilbert's basis theorem Hopkins–Levitzki theorem Krull's principal...

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List of science fiction short stories

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Sampler 1949 Death by Ecstasy Larry Niven Galaxy 1969 Delilah and the Space Rigger Robert A. Heinlein Blue Book 1949 Despoilers of the Golden Empire Randall...

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Diving helmet

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Office, Part 1. The Office. p. 1775 – via University of Minnesota. Savoie, Hilbert Joseph, Jr. Diving gas recovery apparatus. 4,080,964 3-28-78 Cl.128-142...

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