Scielo RSS <![CDATA[Revista mexicana de física E]]> http://www.scielo.org.mx/rss.php?pid=1870-354220130002&lang=pt vol. 59 num. 2 lang. pt <![CDATA[SciELO Logo]]> http://www.scielo.org.mx/img/en/fbpelogp.gif http://www.scielo.org.mx <![CDATA[<b>On average forces and the Ehrenfest theorem for a particle in a semi-infinite interval</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200001&lng=pt&nrm=iso&tlng=pt We study the issues of average forces and the Ehrenfest theorem for a particle restricted to a semi-infinite interval by an impenetrable wall. We consider and discuss two specific cases: (i) a free particle in an infinite step potential, and (ii) a free particle on a half-line. In each situation, we show that the mean values of the position, momentum and force, as functions of time, verify the Ehrenfest theorem (the state of the particle being a general wave packet that is a continuous superposition of the energy eigenstates for the Hamiltonian). However, the involved force is not the same in each case. In fact, we have the usual external classical force in the first case and a type of nonlocal boundary quantum force in the second case. In spite of these different forces, the corresponding mean values of these quantities give the same results. Accordingly, the Ehrenfest equations in the two situations are equivalent. We believe that a careful and clear consideration of how the two cases differ but, in the end, agree, is pertinent, and has not been included in the literature. <![CDATA[<b>Poincaré, la mecánica clásica y el teorema de la recurrencia</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200002&lng=pt&nrm=iso&tlng=pt En conmemoración de los 101 años de la muerte de Henri Poincaré hacemos un recuento de algunas de sus aportaciones a la mecánica clásica aderezándolo con un esbozo de su biografía académica. Usamos de un péndulo para ilustrar la técnica cualitativa para analizar las soluciones a una ecuación dinámica; lo empleamos también, pero suponiéndolo extensible, para ilustrar el uso de los mapeos de Poincaré para diferenciar las soluciones regulares de las caóticas, un tipo de soluciones que el mismo descubrió al estudiar el famoso problema de los tres cuerpos. Demostramos su resultado sobre la recurrencia de las soluciones en un sistema dinámico según el cual toda solución a la que se le exija ser tanto confinada como que conserve la energía deberá de regresar despúes de un tiempo, Tr, a estar tan cerca como se quiera de sus condiciones iniciales. Este es un resultado fundamental que debiera ser más conocido por los estudiantes de física.<hr/>This work commemorates the 101th anniversary of Henri Poincaré's death. We pinpoint his main contributions to classical mechanics while enlivening the discussion with a brief remembrance of his academic career. We employ a physical pendulum for illustrating his techniques for analysing properties of solutions to differential equations without actually solving them. We next use an elastic pendulum for exhibiting how Poincaré maps allow us to distiguish the periodic from the chaotic solutions, a type of solutions which Poincaré himself discovered while studying the famous three body problem. We also give a heuristic proof of his extraordinary recurrence theorem according to which every bound solution of a conservative dynamical system should return, after a time, Tr, to be as close as we like to its initial conditions. We regard this as a very important result that ought to be known by all physics students. <![CDATA[<b>Numerical evaluation of Bessel function integrals for functions with exponential dependence</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200003&lng=pt&nrm=iso&tlng=pt A numerical method for the calculation of Bessel function integrals is proposed for trial functions with exponential type behavior and evaluated for functions with and without explicit exponential dependence. This method utilizes the integral representation of the Bessel function to recast the problem as a double integral; one of which is calculated with Gauss-Chebyshev quadrature while the other uses a parameter-dependent Gauss-Laguerre quadrature in the complex plane. Accurate results can be obtained with relatively small orders of quadratures for the studied classes of functions. <![CDATA[<b>Harmonic oscillator position eigenstates via application of an operator on the vacuum</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200004&lng=pt&nrm=iso&tlng=pt Harmonic oscillator squeezed states are states of minimum uncertainty, but unlike coherent states, in which the uncertainty in position and momentum are equal, squeezed states have the uncertainty reduced, either in position or in momentum, while still minimizing the uncertainty principle. It seems that this property of squeezed states would allow to obtain the position eigenstates as a limiting case, by doing null the uncertainty in position and infinite in momentum. However, there are two equivalent ways to define squeezed states, that lead to different expressions for the limiting states. In this work, we analyze both definitions and show the advantages and disadvantages of using them in order to find position eigenstates. With this in mind, but leaving aside the definitions of squeezed states, we find an operator that applied to the vacuum gives position eigenstates. We also analyze some properties of the squeezed states, based on the new expressions obtained for the eigenstates of the position. <![CDATA[<b>Introduction of the concepts of hole and effective mass using an alternative to the <i>E-k</i> diagram</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200005&lng=pt&nrm=iso&tlng=pt An alternative to the E-k diagram is proposed as a mean of teaching the concept of hole to undergraduate students who have never studied Quantum Mechanics. Some background on the application of Quantum Mechanics to crystalline solids is given in order to discuss the concept of effective mass and the concept of hole. Then, the so-called |p| - ν diagram is geometrically derived from the E-k diagram, using their critical points as a reference. Finally, the new diagram is used as part of a full explanation of the concept of hole and conclusions are given.<hr/>Se propone una alternativa al diagrama E-k como medio de enseñar el concepto de hueco a estudiantes de licenciatura que nunca han estudiado Mecánica Cuántica. Se dan algunos antecedentes sobre la aplicación de la Mecánica Cuántica a sólidos cristalinos necesarios para discutir el concepto de masa efectiva y el concepto de hueco. Después, el llamado diagrama |p| - ν se deriva geométricamente a partir del diagrama E-k, usando sus puntos críticos como referencia. Finalmente, el nuevo diagrama se usa como parte de una explicación completa del concepto de hueco y se sacan algunas conclusiones. <![CDATA[<b>Ninth grade students' mental representations of the refraction of light</b>: <b>didactic implications</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200006&lng=pt&nrm=iso&tlng=pt The study of students' mental representations of physics concepts and phenomena constitutes a central part of physics education research, as they play a decisive role in teaching. In the study presented here, we investigate 213 ninth grade students' mental representations of the phenomenon of refraction, after they were taught about it in school. The empirical data was gathered through an interview using 3 tasks which involved the evaluation of hypothetical situations. The research data included mental representations that cause difficulty in the comprehension of refraction.<hr/>El estudio de representaciones mentales de estudiantes sobre conceptos de Física y fenómenos, constituye una parte central de la investigación en educación física, dado que desemperían un papel decisivo en la enseñanza. En el estudio aquí presentado, se investigan 213 representaciones mentales de estudiantes de noveno grado sobre el fenómeno de la refracción, tras haberles sido enseñado en la escuela. Los datos empíricos fueron recolectados a través de una entrevista utilizando 3 tareas que involucraron la evaluación de situaciones hipotéticas. Los datos de la investigación incluyeron representaciones mentales que causan dificultades en la comprensión de la refracción. <![CDATA[<b>Variational symmetries of Lagrangians</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200007&lng=pt&nrm=iso&tlng=pt We present an elementary derivation of the equation for the infinitesimal generators of variational symmetries of a Lagrangian for a system with a finite number of degrees of freedom. We also give a simple proof of the existence of an infinite number of Lagrangians for a given second-order ordinary differential equation.<hr/>Presentamos una derivación elemental de la ecuación para los generadores infinitesimales de simetrías variacionales de una lagrangiana para un sistema con un número finito de grados de libertad. Damos tambien una prueba simple de la existencia de un número infinito de lagrangianas para una ecuación diferencial ordinaria de segundo orden dada. <![CDATA[<b>En busca de los efectos gravitacionales de Birkhoff</b>: <b>la ultracentrífuga transelástica</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200008&lng=pt&nrm=iso&tlng=pt Este artículo examina el origen, desarrollo, culminación y desenlace del proyecto de la ultracentrífuga transelástica del Centro Nuclear de México ocurridos entre 1971 y 1986. El proyecto tuvo su origen en la búsqueda de un efecto que supuestamente comprobaría la teoría de gravitación de Birkhoff sobre la Relatividad General de Einstein. Para este propósito se diseñó y construyó una extraordinaria ultracentrífuga que mereció el Premio Nacional de Instrumentación (México) 1973. La ultracentrífuga también fue usada para investigar la factibilidad de enriquecer uranio por centrifugación en estado sólido. Se obtuvo uranio altamente enriquecido, aunque en pequeñas cantidades.<hr/>This work reviews the origin, development, completion, and outcome of a trans-elastic ultracentrifuge project of Mexico's Nuclear Center through 1971 to 1986. The project had its origin in the search for an effect that supposedly would validate Birkhoff's gravity theory over Einstein's General Relativity. For this purpose an extraordinary ultracentrifuge was built which deserved the 1973 National Award for Instruments (Mexico). The ultracentrifuge was also used to investigate the feasibility of uranium enrichment by solid state centrifugation. Highly enriched uranium was obtained, but in small quantities. <![CDATA[<b>La red internacional de rayos cósmicos, Manuel Sandoval Vallarta y la física en México</b>]]> http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422013000200009&lng=pt&nrm=iso&tlng=pt En 1932 Arthur Holly Compton organizó una gran expedición por el norte de Canadá, Michigan, Illinois, Hawaii, Nueva Zelanda, Australia, Perú y México con el propósito de establecer una red internacional de estaciones de rayos cósmicos para estudiar la distribución geográfica de los rayos cósmicos. En esta expedición se coordinó a un grupo de especialistas distribuidos por distintas rutas de viaje. Para organizar la red de rayos cósmicos fue necesario establecer contactos con personas e instituciones en los lugares donde se iban a tomar las medidas. Además, se requirió de la construcción y estandarización de los instrumentos científicos y las técnicas para tomar medidas. La circulación de instrumentos científicos, personas y prácticas fueron esenciales para llevar a cabo esta expedición. México fue uno de los lugares donde habrían de tomarse medidas de intensidad de rayos cósmicos. Esto ocurrió con la intervención de Manuel Sandoval Vallarta, quien en ese momento era profesor asociado del Massachusetts Institute of Technology (MIT), y con la colaboración de un grupo de ingenieros de la Universidad Nacional Autónoma de México. A finales de la década de los 30s esta colaboración se convirtió en un factor clave para la creación del primer instituto de física en México.<hr/>As part of the establishment of an international cosmic ray network for studying the geographical distribution of cosmic rays, in 1932 Arthur Holly Compton organized a huge expedition to North Canada, Michigan, Illinois, Hawaii, New Zealand, Australia, Peru, and Mexico. In this expedition a group of experts was coordinated and distributed by different travel routes.For arranging this cosmic ray network it was necessary to contact with people and institutions at the local places where the measurements were to be taken. Also,it was implied the construction and standardization of instruments, as well as the techniques to take measurements. Circulation of scientific instruments, persons and practices were essential for executing the expedition. Mexico was one of the places where the cosmic ray measurements were taken. It was through intervention of Manuel Sandoval Vallarta (who at the moment was Associate Professor of the Physics Department at the MIT) that this could be done. Also, a group of engineers from the University of Mexico participated in this task. At the end of the thirties, this collaboration was used as a key factor for the creation of the first institute of physics in Mexico.