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Rigged Hilbert spaces in quantum mechanics

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Abstract

It is shown how rigged Hilbert spaces may be constructed in quantum mechanics, and the properties of the resulting spaces are derived. The theory is applied to non-relativistic quantum systems ofn interacting particles. The spectral theory in rigged Hilbert spaces is developed and the results necessary for the application to the Dirac formalism are derived.

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Authors and Affiliations

  1. Emmanuel College, Cambridge

    J. E. Roberts

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  1. J. E. Roberts
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The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research under Grant AF EOAR 65–36, through the European Office of Aerospace Research (OAR), United States Air Force.

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Roberts, J.E. Rigged Hilbert spaces in quantum mechanics. Commun.Math. Phys. 3, 98–119 (1966). https://doi.org/10.1007/BF01645448

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