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 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

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 $+i \epsilon$ prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman's $+i \epsilon$ 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

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