4,343 research outputs found
The Abell 85 BCG: a nucleated, core-less galaxy
New high-resolution r band imaging of the brightest cluster galaxy (BCG) in
Abell 85 (Holm 15A) was obtained using the Gemini Multi Object Spectrograph.
These data were taken with the aim of deriving an accurate surface brightness
profile of the BCG of Abell 85, in particular its central region. The new
Gemini data show clear evidence of a previously unreported nuclear emission
that is evident as a distinct light excess in the central kiloparsec of the
surface brightness profile. We find that the light profile is never flat nor
does it present a downward trend towards the center of the galaxy. That is, the
new Gemini data show a different physical reality from the featureless,
"evacuated core" recently claimed for the Abell 85 BCG. After trying different
models, we find that the surface brightness profile of the BCG of Abell 85 is
best fit by a double Sersic model.Comment: Gemini web feature: Supermassive black hole that wasn't -
http://gemini.edu/node/1247
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 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
On the inconsistency of the Bohm-Gadella theory with quantum mechanics
The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum
Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom
asserts that the solutions of the Lippmann-Schwinger equation are functionals
over spaces of Hardy functions. The preparation-registration arrow of time
provides the physical justification for the Hardy axiom. In this paper, it is
shown that the Hardy axiom is incorrect, because the solutions of the
Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also
shown that the derivation of the preparation-registration arrow of time is
flawed. Thus, Hardy functions neither appear when we solve the
Lippmann-Schwinger equation nor they should appear. It is also shown that the
Bohm-Gadella theory does not rest on the same physical principles as quantum
mechanics, and that it does not solve any problem that quantum mechanics cannot
solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page
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 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
Rigged Hilbert Space Approach to the Schrodinger Equation
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 Schrodinger Hamiltonians whose spectrum has a
continuous part are disclosed. Those difficulties are overcome by using an
appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an
eigenket to each energy in the spectrum of the Hamiltonian, regardless of
whether the energy belongs to the discrete or to the continuous part of the
spectrum. The collection of eigenkets corresponding to both discrete and
continuous spectra forms a basis system that can be used to expand any physical
wave function. Thus the RHS treats discrete energies (discrete spectrum) and
scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page
Simple Pendulum Revisited
We describe a 8085 microprocessor interface developed to make reliable time
period measurements. The time period of each oscillation of a simple pendulum
was measured using this interface. The variation of the time period with
increasing oscillation was studied for the simple harmonic motion (SHM) and for
large angle initial displacements (non-SHM). The results underlines the
importance of the precautions which the students are asked to take while
performing the pendulum experiment.Comment: 17 pages with 10 figure
The role of the rigged Hilbert space in Quantum Mechanics
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. In particular, Dirac's bra-ket formalism is
fully implemented by the rigged Hilbert space rather than just by the Hilbert
space. In this paper, we provide a pedestrian introduction to the role the
rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly
solvable example. The procedure will be constructive and based on a recent
publication. We also provide a thorough discussion on the physical significance
of the rigged Hilbert space.Comment: 29 pages, 2 figures; a pedestrian introduction to the rigged Hilbert
spac
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