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Resonances, scattering theory and rigged Hilbert spaces. [Survival amplitude, Cauchy theorem]
Giuseppe Pastori Parravicini+2 more
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The Rigged Hilbert Space Formulation of Quantum Mechanics and its Implications for Irreversibility
Christoph Schulte+2 more
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A rigged Hilbert space for the free radiation field
Journal of Mathematical Physics, 1985We here construct a rigged Hilbert space suitable for the description of the free radiation field in a box and in the Coulomb gauge. We prove the continuity of the main observables on this structure.
M. Gadella
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Gamow States in a Rigged Hilbert Space
, 1998The space of analytical test functions rapidly decreasing on the real axis (i.e: Schwartz test functions on the real axis), is used to construct the Rigged Hilbert Space (RHS) where Resonant Gamow States (GS) are defined starting from Dirac’s formula. It is shown that the expectation value of a self-adjoint operator acting on a GS is real.
C. G. Bollini+3 more
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Resonance poles and Gamow vectors in the rigged Hilbert space formulation of quantum mechanics
, 1981After a summary of the Rigged Hilbert space formulation of quantum mechanics and a brief statement of its advantages over von Neumann’s formulation, a mathematically correct definition of Gamow’s exponentially decaying vectors as generalized energy ...
A. Bohm
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, 1974
Roberts' proposal of a rigged Hilbert space Φ⊂G⊂Φ× for a certain class of quantum systems is reinvestigated and developed in order to exhibit various properties of this kind of rigged Hilbert spaces which might be of interest for the application of this ...
O. Melsheimer
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Roberts' proposal of a rigged Hilbert space Φ⊂G⊂Φ× for a certain class of quantum systems is reinvestigated and developed in order to exhibit various properties of this kind of rigged Hilbert spaces which might be of interest for the application of this ...
O. Melsheimer
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The Lippmann-Schwinger equations in the rigged Hilbert space
Journal of Physics A: Mathematical and General, 2002We give a rigorous meaning to the Lippmann-Schwinger equations relating generalized eigenvectors of the free and perturbed Hamiltonians in a scattering process. Some related formulae are also presented. A discussion is made on the context of rigged Hilbert space formulation of quantum mechanics.
M. Gadella, F. Gómez
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