The role of the rigged Hilbert space in quantum mechanics

By R. Madrid. 2005

203 citations recorded by the source corpus.

There is compelling evidence that, when a continuous spectrum is present, the natural mathematical setting for quantum mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in quantum mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/17975202ffca3ee435e1736aa3860007427cac24

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei (2015, background): “wave, because plane waves states are not contained in the Hilbert space of square-integrable wave functions8. 8To properly work with such states, a rigged Hilbert space must be introduced (see, e.g., [116] and references therein). 59 In practical calculations, we can only work with ﬁnite localized s”