1,158 research outputs found
The time-dependent Schrödinger equation: the need for the Hamiltonian to be self-adjoint
We present some simple arguments to show that quantum mechanics operators are required to be self-adjoint. We emphasize that the very definition of a self-adjoint operator includes the prescription of a certain domain of the operator. We then use these concepts to revisit the solutions of the time-dependent Schroedinger equation of some well-known simple problems - the infinite square well, the finite square well, and the harmonic oscillator. We show that these elementary illustrations can be enriched by using more general boundary conditions, which are still compatible with self-adjointness. In particular, we show that a puzzling problem associated with the Hydrogen atom in one dimension can be clarified by applying the correct requirements of self-adjointness. We then come to Stone\'s theorem, which is the main topic of this paper, and which is shown to relate the usual definitions of a self-adjoint operator to the possibility of constructing well-defined solutions of the time-dependent Schrödinger equation.Conselho Nacional de Desenvolvimento Cientà fico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP
Guided Unfoldings for Finding Loops in Standard Term Rewriting
In this paper, we reconsider the unfolding-based technique that we have
introduced previously for detecting loops in standard term rewriting. We
improve it by guiding the unfolding process, using distinguished positions in
the rewrite rules. This results in a depth-first computation of the unfoldings,
whereas the original technique was breadth-first. We have implemented this new
approach in our tool NTI and compared it to the previous one on a bunch of
rewrite systems. The results we get are promising (better times, more
successful proofs).Comment: Pre-proceedings paper presented at the 28th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt
am Main, Germany, 4-6 September 2018 (arXiv:1808.03326
The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model
The dynamics of wave packets in a relativistic Dirac oscillator is compared
to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the
Dirac oscillator produces the entanglement of the spin with the orbital motion
similar to what is observed in the model of quantum optics. The collapses and
revivals of the spin which result extend to a relativistic theory our previous
findings on nonrelativistic oscillator where they were known under the name of
`spin-orbit pendulum'. There are important relativistic effects (lack of
periodicity, zitterbewegung, negative energy states). Many of them disappear
after a Foldy-Wouthuysen transformation.Comment: LaTeX2e, uses IOP style files (included), 14 pages, 9 separate
postscript figure
Relativistic confinement of neutral fermions with a trigonometric tangent potential
The problem of neutral fermions subject to a pseudoscalar potential is
investigated. Apart from the solutions for , the problem is
mapped into the Sturm-Liouville equation. The case of a singular trigonometric
tangent potential () is exactly solved and the
complete set of solutions is discussed in some detail. It is revealed that this
intrinsically relativistic and true confining potential is able to localize
fermions into a region of space arbitrarily small without the menace of
particle-antiparticle production.Comment: 12 page
Identifying resources used by young people to overcome mental distress in three Latin American cities: a qualitative study
OBJECTIVE: To explore which resources and activities help young people living in deprived urban environments in Latin America to recover from depression and/or anxiety. DESIGN: A multimethod, qualitative study with 18 online focus groups and 12 online structured group conversations embedded into arts workshops. SETTING: This study was conducted in Bogotá (Colombia), Buenos Aires (Argentina) and Lima (Peru). PARTICIPANTS: Adolescents (15–16 years old) and young adults (20–24 years old) with capacity to provide assent/consent and professionals (older than 18 years of age) that had experience of professionally working with young people were willing to share personal experience within a group, and had capacity to provide consent. RESULTS: A total of 185 participants took part in this study: 111 participants (36 adolescents, 35 young adults and 40 professionals) attended the 18 focus groups and 74 young people (29 adolescents and 45 young adults) took part in the 12 arts workshops. Eight categories captured the resources and activities that were reported by young people as helpful to overcome mental distress: (1) personal resources, (2) personal development, (3) spirituality and religion, (4) social resources, (5) social media, (6) community resources, (7) activities (subcategorised into artistic, leisure, sports and outdoor activities) and (8) mental health professionals. Personal and social resources as well as artistic activities and sports were the most common resources identified that help adolescents and young adults to overcome depression and anxiety. CONCLUSION: Despite the different contexts of the three cities, young people appear to use similar resources to overcome mental distress. Policies to improve the mental health of young people in deprived urban settings should address the need of community spaces, where young people can play sports, meet and engage in groups, and support community organisations that can enable and facilitate a range of social activities
Controlling a resonant transmission across the -potential: the inverse problem
Recently, the non-zero transmission of a quantum particle through the
one-dimensional singular potential given in the form of the derivative of
Dirac's delta function, , with , being a
potential strength constant, has been discussed by several authors. The
transmission occurs at certain discrete values of forming a resonance
set . For
this potential has been shown to be a perfectly reflecting wall. However, this
resonant transmission takes place only in the case when the regularization of
the distribution is constructed in a specific way. Otherwise, the
-potential is fully non-transparent. Moreover, when the transmission
is non-zero, the structure of a resonant set depends on a regularizing sequence
that tends to in the sense of
distributions as . Therefore, from a practical point of
view, it would be interesting to have an inverse solution, i.e. for a given
to construct such a regularizing sequence
that the -potential at this value is
transparent. If such a procedure is possible, then this value
has to belong to a corresponding resonance set. The present paper is devoted to
solving this problem and, as a result, the family of regularizing sequences is
constructed by tuning adjustable parameters in the equations that provide a
resonance transmission across the -potential.Comment: 21 pages, 4 figures. Corrections to the published version added;
http://iopscience.iop.org/1751-8121/44/37/37530
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