Results 1 to 10 of about 77,076 (114)

The role of the rigged Hilbert space in Quantum Mechanics [PDF]

, 2005
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.
Atkinson D, Ballentine L E, Beyer R T, Bogolubov N N, Bohm A, Bohm A, Bohm A, Capri A Z, Cohen-Tannoudji C, de la Madrid R, de la Madrid R, de la Madrid R, de la Madrid R, Dirac P A M, Dubin D A, Galindo A, Gelfand I M, Kukulin V I, Maurin K, Rafael de la Madrid, Reed M, Roberts J E, Schwartz L, Suchanecki Z, von Neumann J   +24 more
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Rigged Hilbert Space Approach to the Schrodinger Equation [PDF]

, 2001
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
Antoine J P, Antoine J P, Antoine J P, Antoniou I, Bohm A, Bohm A, Bohm A, de la Madrid R, de la Madrid R, Dunford N, Galindo A, Gelfand I M, Hernández E, Kristensen P, Kristensen P, Kukulin V I, Maurin K, Mejlbo L C, Melsheimer O, Mondragón A, Newton R G, Newton R G, Nussenzveig H M, R de la Madrid, Roberts J E, Roberts J E, Taylor J R, Von Neumann J   +27 more
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Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics [PDF]

, 2002
We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous ...
A Bohm, Antoine J P, Antoine J P, Antoine J P, Bohm A, Bohm A, Bohm A, Bohm A, Bohm A, Bohm A, Flato M, Hille E, Komura T, Nagel B, Nelson E, Pietsch A, Roberts J E, Robinson D, Robinson D, Rusinek J, S Wickramasekara, Simon J, Yosida K   +22 more
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Description of resonances within the rigged Hilbert space [PDF]

, 2006
The spectrum of a quantum system has in general bound, scattering and resonant parts. The Hilbert space includes only the bound and scattering spectra, and discards the resonances.
de la Madrid, R.
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The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I [PDF]

, 2006
We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their time evolution ...
Amrein W, Bohm A, Bohm A R de la Madrid R Tay B A Kielanowski P, de la Madrid R, de la Madrid R, de la Madrid R, de la Madrid R, de la Madrid R, Dunford N, Gadella M, Gelfand I M, Goldberger M L, Kato T, Maurin K, Newton R G, Rafael de la Madrid, Reed M, Taylor J R   +17 more
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Quantum Mechanics and Its Evolving Formulations [PDF]

Entropy, 2021
In this paper, we discuss the time evolution of the quantum mechanics formalism. Starting from the heroic beginnings of Heisenberg and Schrödinger, we cover successively the rigorous Hilbert space formulation of von Neumann, the practical bra-ket ...
Jean-Pierre Antoine
doaj   +2 more sources

Mathematical Models for Unstable Quantum Systems and Gamow States [PDF]

Entropy, 2022
We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems.
Manuel Gadella, Sebastián Fortín, Juan Pablo Jorge, Marcelo Losada   +3 more
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Operators in Rigged Hilbert Spaces, Gel’fand Bases and Generalized Eigenvalues [PDF]

Mathematics, 2022
Given a self-adjoint operator A in a Hilbert space H, we analyze its spectral behavior when it is expressed in terms of generalized eigenvectors.
Jean-Pierre Antoine, Camillo Trapani
doaj   +2 more sources

Groups, Special Functions and Rigged Hilbert Spaces [PDF]

Axioms, 2019
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality.
Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo   +2 more
doaj   +3 more sources

Riesz-like bases in rigged Hilbert spaces

, 2015
The notions of Bessel sequence, Riesz-Fischer sequence and Riesz basis are generalized to a rigged Hilbert space $\D[t] \subset \H \subset \D^\times[t^\times]$. A Riesz-like basis, in particular, is obtained by considering a sequence $\{\xi_n\}\subset \D$
Bellomonte, Giorgia, Trapani, Camillo
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