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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. They bring together the 'bound state' (eigenvector) and 'continuous spectrum', in one place.
Using this notion, a version of the spectral theorem for unbounded operators on Hilbert space can be formulated.[1] "Rigged Hilbert spaces are well known as the structure which provides a proper mathematical meaning to the Dirac formulation of quantum mechanics."[2]
- ^ Minlos, R. A. (2001) [1994], "Rigged_Hilbert_space", Encyclopedia of Mathematics, EMS Press
- ^ Krasnoholovets, Volodymyr; Columbus, Frank H. (2004). New Research in Quantum Physics. Nova Science Publishers. p. 79. ISBN 978-1-59454-001-1.