 02209 R de la Madrid
 Rigged Hilbert Space Approach to the Schrodinger Equation
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May 1, 02

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Abstract. It is shown that the natural framework for the solutions of any
Schrodinger equation whose spectrum has a continuous part is the Rigged
Hilbert Space rather than just the Hilbert space. The difficulties of
using only the Hilbert space to handle unbounded Schrodinger
Hamiltonians whose spectrum has a continuous part are disclosed. Those
difficulties are overcome by using an appropriate Rigged Hilbert Space
(RHS). The RHS is able to associate an eigenket to each energy in the
spectrum of the Hamiltonian, regardless of whether the energy belongs
to the discrete or to the continuous part of the spectrum. The
collection of eigenkets corresponding to both discrete and continuous
spectra forms a basis system that can be used to expand any physical
wave function. Thus the RHS treats discrete energies (discrete spectrum)
and scattering energies (continuous spectrum) on the same footing.
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