The role of the rigged Hilbert space in Quantum Mechanics

Abstract

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.

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

References in corpus (4)

• Rigged Hilbert Space Treatment of Continuous Spectrum
• Rigged Hilbert Space Approach to the Schrodinger Equation
• The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential
• The Rigged Hilbert Space of the Free Hamiltonian

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