200 citations · 350 across the 18 of their papers we have counts for
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Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential
Rafael de la Madrid
We express the resonant energies of the delta-shell potential in terms of the Lambert function, and we calculate their decay widths and decay constants. The ensuing numerical r…
Reply to Comment arXiv:0704.3529v1
R. de la Madrid
In this reply, we show that the author of the Comment arXiv:0704.3529v1 inadvertently provides additional arguments against the use of Hardy functions as test functions for the Gam…
Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''
R. de la Madrid
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…
A selfadjoint variant of the time operator
R. de la Madrid, J. M. Isidro
We study the selfadjoint time operator recently constructed by one of the authors. We will show that this time operator must be interpreted as a ``selfadjoint variant'' of the time…
Description of resonances within the rigged Hilbert space
R. de la Madrid
The spectrum of a quantum system has in general bound, scattering and resonant parts. The Hilbert space includes only the bound and scattering spectra, and discards the resonances.…
On the inconsistency of the Bohm-Gadella theory with quantum mechanics
R. de la Madrid
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 solution…
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
R. de la Madrid
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 rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
R. de la Madrid
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 bra…
Localization of non-relativistic particles
R. de la Madrid
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in…
Resonance expansions in quantum mechanics
R. de la Madrid, G. Garcia-Calderon, J. G. Muga
The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature.
On the connection between the Schrodinger and the Heisenberg pictures for unbounded operators
R. de la Madrid
It is well known that the unboundedness of operators in Hilbert space entails domain troubles. It is also well known that most domain troubles can be surmounted by extending the Hi…
The role of the rigged Hilbert space in Quantum Mechanics
R. de la Madrid
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 Hilb…
The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential
R. de la Madrid
The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential is constructed. The one-dimensional rectangular potential provides another opportunity…
Two analytic continuations of the Lippmann-Schwinger eigenfunctions
R. de la Madrid
We first present two possible analytic continuations of the Lippmann-Schwinger eigenfunctions to the second sheet of the Riemann surface, and then we compare the different Gamow ve…
The Rigged Hilbert Space of the Free Hamiltonian
R. de la Madrid
We explicitly construct the Rigged Hilbert Space (RHS) of the free Hamiltonian . The construction of the RHS of provides yet another opportunity to see that when continu…