3,478 research outputs found
Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''
In this reply, we show that when we apply standard distribution theory to the
Lippmann-Schwinger equation, the resulting spaces of test functions would
comply with the Hardy axiom only if classic results of Paley and Wiener, of
Gelfand and Shilov, and of the theory of ultradistributions were wrong. As
well, we point out several differences between the ``standard method'' of
constructing rigged Hilbert spaces in quantum mechanics and the method used in
Time Asymmetric Quantum Theory.Comment: 13 page
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
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 and the rigged Hilbert spaces to
which they belong. It will be concluded that the natural setting for the
solutions of the Lippmann-Schwinger equation--and therefore for scattering
theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur
Primers resultats de l'estudi de la cerà mica terra sigillata de Baetulo: circulació cerà mica i aportacions cronològiques a la ciutat
Les actuacions arqueologiques portades a terme des dels anys se tanta a la ciutat de Badalona, han permes posar al descobert una part important d'estructures corresponents a la ciutat romana de Baetulo. A partir d'aquestes excavacions, l' analisi especĂfica de la ceramica terra sigillata documentada en determinats contextos estratigrafics, on aquest tipus ceramic Ă©s l'element basic de dataciĂł, ens ha permes realitzar una revisiĂł de les cronologies proposades inicialment per a aquests estrats i per a les estructures associades. Aquesta revisiĂł, que afecta el perĂode que va del regnat d' August fms a epoca flavia, ha suposat la clarificaciĂł del material de terra sigillata recuperat i, en alguns casos, la modificaciĂł de la interpretaciĂł de la seqĂĽencia estratigrafica i la se va dataciĂł
F-transforms for the definition of contextual fuzzy partitions
Fuzzy partitions can be defined in many different ways, but usually, it is done taking into account the whole universe. In this paper, we present a method to define fuzzy partitions according to those elements in the universe holding certain fuzzy attribute. Specifically, we show how to define those fuzzy partitions by means of F-transforms.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
This work has been partially supported by the Spanish Ministry of Science by the projects TIN15-70266-C2-P-1 and TIN2016-76653-
The non-equilibrium work relation. Thermodynamic analysis and microscopic foundations
We discuss the conditions for which the non-equilibrium work relation is
valid by means of thermodynamic and microscopic arguments.Comment: 16 pages 1 figur
The Importance of Boundary Conditions in Quantum Mechanics
We discuss the role of boundary conditions in determining the physical
content of the solutions of the Schrodinger equation. We study the
standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary
conditions. As well, we rephrase Feynman's prescription as a
time-asymmetric, causal boundary condition, and discuss the connection of
Feynman's prescription with the arrow of time of Quantum
Electrodynamics. A parallel of this arrow of time with that of Classical
Electrodynamics is made. We conclude that in general, the time evolution of a
closed quantum system has indeed an arrow of time built into the propagators.Comment: Contribution to the proceedings of the ICTP conference "Irreversible
Quantum Dynamics," Trieste, Italy, July 200
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
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 space rather than just the Hilbert space. It is also argued
that this analytic continuation entails the imposition of a time asymmetric
boundary condition upon the group time evolution, resulting into a semigroup
time evolution. Physically, the semigroup time evolution is simply a (retarded
or advanced) propagator.Comment: 32 pages, 3 figure
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