Results 11 to 20 of about 2,208 (153)
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 +2 more
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Rigged Hilbert space approach to the Schrödinger equation [PDF]
Journal of Physics A: Mathematical and General, 2002 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
Rafael de la Madrid
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Groups, Jacobi functions, and rigged Hilbert spaces [PDF]
Journal of Mathematical Physics, 2020 This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations of their ...
E. Celeghini, M. Gadella, M. A. del Olmo
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Description of Resonances within the Rigged Hilbert Space [PDF]
AIP Conference Proceedings, 2007 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.
Rafael de la Madrid
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Operators in Rigged Hilbert spaces: some spectral properties [PDF]
Journal of Mathematical Analysis and Applications, 2013 A notion of resolvent set for an operator acting in a rigged Hilbert space $\D \subset \H\subset \D^\times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $\D$ and $\D^\times$, called interspaces.
Giorgia Bellomonte +2 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
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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
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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 +3 more
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Quantum optical phase, rigged Hilbert spaces and complementarity. [PDF]
Philos Trans A Math Phys Eng SciWe place Loudon’s quantum treatment of optical phase in The quantum theory of light in its historical context, and outline research that it inspired. We show how it led Pegg and Barnett to their quantum phase formalism, explaining the challenges that they overcame to define phase operators and phase eigenstates ...
Bordon K, Vaccaro JA.
europepmc +5 more sources
SU(2), Associated Laguerre Polynomials and Rigged Hilbert Spaces [PDF]
, 2018 We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the Laguerre polynomials. These functions are similar to the spherical harmonics defined on the sphere.
E. Celeghini, M. Gadella, M. A. del Olmo
openalex +7 more sources