An alternative algebraic method for solving the radial equation for the hidrogen atom

Dos operadores de escalera se introducen  para resolver la ecuación radial del átomo de hidrógeno. Los valores propios de energía, así explícitas expresiones analíticas para las funciones propias de este problema particular, Kepler se obtienen después de un poco de manipulación algebraica de los operadores

Desarrollo y evaluación de un dispositivo electrónico de peso ligero para el muestreo de compuestos orgánicos volátiles en la vertical acoplado a un globo meteorológico cautivo

An understanding of the vertical profile of the composition of volatile organic compounds (VOCs) in polluted urban areas can help to better understand the impact of these compounds on air quality and in the development of better control strategies. To facilitate these types of measurements and they have the necessary reliability, a programmable, lightweight and lowcost VOCs miniaturized sampling device was designed and integrated, that allows to anchor several of them at different heights in the string of a captive instrumented meteorological balloon and also a start/stop control of the samplers that can be operated from the ground. Simultaneous sampling ensures that the vertical profile of the captured VOCs, represents with better certainty the expected differences in the concentration of these compounds due to the influence of the urban canopy layer and urban activity. Each sampling device consists of an electronic circuit that receives the start or stop signal of the air suction mini-pump from a master control system that is on the surface and that allows radio frequency operation. The capture of VOCs is carried out by packed cartridges with an appropriated adsorbent medium for this purpose. The feasibility of the miniaturized system was demonstrated in a short sampling campaign at the levels 0 m, 50 m, and 100 m above ground at a site southwest of the Metropolitan Area of Mexico City during April 2017. The profiles of the determined VOCs concentrations were compared with previous records obtained at the surface level and in vertical profiles using less dynamic sampling methods, demonstrating the benefit of knowing the concentration at different heights in the interpretation of atmospheric chemistry associated with these profiles.El conocimiento del perfil vertical de la composición de los compuestos orgánicos volátiles (COVs) en áreas urbanas contaminadas puede ayudar a un mejor entendimiento del impacto de estos compuestos en la calidad del aire y en el desarrollo de mejores estrategias de control. Con el fin facilitar este tipo de mediciones y de que éstas tengan la confiabilidad necesaria, se diseñó e integró un dispositivo de muestreo miniaturizado programable de COVs ligero de bajo costo, que permite el anclaje de varios de ellos a diversos niveles de altura en el cordel de un globo meteorológico cautivo instrumentado, y cuyo arranque y paro de los muestreadores es controlado desde superficie. El muestreo simultáneo asegura que el perfil vertical de los COVs capturados representen con mejor certeza las diferencias esperadas en la concentración de estos compuestos debido a la influencia del dosel urbano y de la actividad urbana. Cada dispositivo de muestreo consiste en un circuito electrónico que recibe la señal de arranque y/o paro de la minibomba de succión de aire de un sistema maestro de control que se ubica en superficie y que comanda la operación por radiofrecuencia. La captura de los COVs es realizada por medio de un cartucho empacado con un medio adsorbente apropiado para este objeto. La aplicabilidad del sistema miniaturizado fue demostrada en una campaña corta de muestreos a los niveles 0 m, 50 m, y 100 m sobre la superficie en un sitio al suroeste de la Zona Metropolitana de la Ciudad de México durante abril de 2017. Los perfiles de las concentraciones de COVs determinadas fueron comparados tanto con registros previos obtenidos a nivel superficie como en perfiles verticales utilizando métodos de muestreo menos dinámicos demostrando así el beneficio de conocer la concentración a diferentes alturas en la interpretación de la química atmosférica asociada a estos perfiles

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Spiked oscillators: exact solution

A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators

A basis for variational calculations in d dimensions

In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions. The basis functions in each angular momentum subspace are of the form phi_i(r)=r^{i+1+(t-d)/2}e^{-r^p/2}, i >= 0, p > 0, t > 0. The matrix elements are given in terms of the Gamma function for all d. The significance of the parameters t and p and scale s are discussed. Applications to a variety of potentials are presented, including potentials with singular repulsive terms of the form b/r^a, a,b > 0, perturbed Coulomb potentials -D/r + B r + Ar^2, and potentials with weak repulsive terms, such as -g r^2 + r^4, g > 0.Comment: 22 page

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum