Results 21 to 30 of about 2,208 (153)
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 ...
S. Wickramasekara, Arno Böhm
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Riesz-like bases in rigged Hilbert spaces [PDF]
Zeitschrift für Analysis und ihre Anwendungen, 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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The Rigged Hilbert Space of the Free Hamiltonian [PDF]
International Journal of Theoretical Physics, 2003 We explicitly construct the Rigged Hilbert Space (RHS) of the free Hamiltonian $H_0$. The construction of the RHS of $H_0$ provides yet another opportunity to see that when continuous spectrum is present, the solutions of the Schrodinger equation lie in ...
de la Madrid, R.
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Unified exact WKB framework for resonance — Zel’dovich/complex-scaling regularization and rigged Hilbert space — [PDF]
Journal of High Energy PhysicsWe develop a unified framework for analyzing quantum mechanical resonances using the exact WKB method. The non-perturbative formulation based on the exact WKB method works for incorporating the Zel’dovich regularization, the complex scaling method, and ...
Okuto Morikawa, Shoya Ogawa
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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.
Rafael de la Madrid
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The rigged Hilbert space approach to the Lippmann–Schwinger equation: II. The analytic continuation of the Lippmann–Schwinger bras and kets [PDF]
, 2006 The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert ...
Rafael de la Madrid
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Rigged Hilbert spaces and contractive families of Hilbert spaces [PDF]
Monatshefte für Mathematik, 2010 15 pages.
Giorgia Bellomonte, Camillo Trapani
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Zernike functions, soft adaptive optics and rigged Hilbert spaces [PDF]
Journal of Mathematical Physics, 2019 We revise the symmetries of the Zernike polynomials that determine the Lie algebra su(1, 1) ⊕ su(1, 1). We show how they induce discrete as well as continuous bases that coexist in the framework of rigged Hilbert spaces. We also discuss some other interesting properties of Zernike polynomials and Zernike functions.
E. Celeghini, M. Gadella, M. A. del Olmo
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Computing Generalized Eigenfunctions in Rigged Hilbert Spaces [PDF]
Pure and Applied AnalysisWe introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions, such as asymptotics or other analytic properties. Instead, we carefully sample the range of the resolvent operator
Matthew J. Colbrook +2 more
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