The role of the rigged Hilbert space in Quantum Mechanics

Details The role of the rigged Hilbert space in Quantum Mechanics The role of the rigged Hilbert space in Quantum Mechanics

2005-02-09

arxiv.org/abs/quant-ph/0502053v1

Eur. J. Phys. 26 (2005) 287-312

Physics

Quantum Physics

29 pages, 2 figures; a pedestrian introduction to the rigged Hilbert space

Scientific paper

10.1088/0143-0807/26/2/008

There is compelling evidence that, when 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.

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