Vol. 54 No. 1 Jan-Jun (2008): Revista Mexicana de Física E
Published:
2008-01-01
Artículos
-
Impenetrable barriers in quantum mechanics
Abstract:We derive the expression $V(x)\,u(x) = c\,\delta (x - a) + v(x)\,u(x)$ (where $V(x)$ is the potential, $u(x)$ the wave function, $c$ a constant and $v(x)$ a finite potential function for $x \le a)$, which is present in the one-dimensional Schrödinger equation on the whole real line when we have an impenetrable barrier at $x \ge a$, that is, an infinite step potential there. By studying the solution of this equation, we identify, connect and discuss three different Hamiltonian operators that describe the barrier. We extend these results by constructing an infinite square-well potential from two impenetrable barriers.⬇️ Scroll down to see the full summary -
Students' understanding of vectors in the context of forces
Abstract:A functional understanding of Newton's second law as a vector equation requires that students be able to reason about forces as vectors. In this paper, we present data describing students' conceptual difficulties with forces as vectors. These data suggest that after traditional instruction in introductory physics, some students do not recognize the vector nature of this quantity. Other students do not have the necessary procedural knowledge to determine net force or acceleration, and are therefore unable to reason qualitatively about Newton's second law. We describe some specific procedural and reasoning difficulties we have observed in the students' use of vectors in the context of forces and Newton's second law. In addition, we encourage modifications in the instruction of mechanics that we designed on the basis of our research into student understanding. These modifications are intended to improve the students' understanding of vector addition and subtraction and to promote the students' use of vectors insolving mechanics problems.⬇️ Scroll down to see the full summary -
Thermal model for a microhot plate used in a MEM gas sensor
Abstract:A thermal analytical model for a MEM gas sensor is presented and compared with an electrical circuit equivalent model. The objective is to study the temperature performance of the microhot plate configured within a MEM structure used for gas sensing. From this, it is possible to determine the magnitude of the electrical current that must be applied to the polysilicon heater on regard of its dimensions and materials used, for instance, when the sensor structure is fabricated with a MEMS technology compatible with CMOS integrated circuits fabrication. Results are presented where the response time and temperature level, as a function of applied current, can be determined. The model presented can be used as a base for designing microhot plates operating in gas sensors, where temperatures in the order of 300$^\circ$C are needed and that will be integrated monolithically with associated electronics, with constraints as minimum power dissipation.⬇️ Scroll down to see the full summary -
Color centers envisioned as confined quantum systems: the case of F, F' and F$_{2}^{+}$ centers
Abstract:Color centers in alkali halides, as well as point defects with dimensions of a few nanometers, have been considered to be confined systems and were studied with a variational formalism within a semi-continuum model. This new approach was applied to the well-known F, F' and F$_{2}^{+}$ centers, which are assumed to be cavities of a determined shape that can trap one or two electrons. Inside of the cavity, the electron is subject to a constant potential ($V_{0}$) related to the Madelung energy and outside of it, the potential is Coulomb type due to a continuum polarizable medium. Because the F, F' and F$_{2}^{+}$ confined systems were considered to be hydrogen-like, helium-like and H$_{2}^{+}$-like molecular ion systems, respectively, the \emph{ansatz} functions were constructed from wave functions corresponding to these kinds of systems. For these systems, the energy transition ($\Delta E$) from the ground state to the first excited state in KCl crystals was calculated and compared with experimental and calculated values obtained from the literature. The $\Delta E$ behavior is shown for different values of $V_{0}$. It is worth mentioning that the formalism presented in this work would be useful for both graduate and undergraduate students embarking on the study of some properties of confined quantum systems, or some simple nanostructures as well.⬇️ Scroll down to see the full summary -
Simple deductions of the integral representations of the relativistic Faraday and Ampère-Maxwell laws and the relativistic transformation laws of the electromagnetic field
Abstract:By using simple concepts of special relativity and the differential representations of the Faraday and Ampère-Maxwell laws, we deduce their Gelman-Monsivais integral representation. The relativistic transformation laws of the electromagnetic field are also obtained without using tensorial analysis or covariant concepts.⬇️ Scroll down to see the full summary -
Sobre la ecuación de transferencia radiativa relativista especial
Abstract:The purpose is to introduce in a clear and direct way the students of undergraduate courses in physics and/or astronomy to the subject of radiative transfer. A pedagogical revision is made in order to obtain the radiative transfer equation, its restrictions and the different types of interactions present between the radiation and the matter. Because in the classical literature about radiative transfer the covariance is not fully developed, we show in an explicit manner detail calculations and then we discuss the relativistic effects.⬇️ Scroll down to see the full summary -
Energética de la contracción muscular en el régimen de operación ecológico
Abstract:In this work muscular contraction is studied using linear irreversible thermodynamics and the ecological regime of operation as a theoretical frameworks. From the results obtained, it is concluded that the ecological regime of operation does not represent a good approach between potency and the efficiency of the muscle. This suggests that the ecological regime of operation is not a good theoretical framework to model the muscular energy.⬇️ Scroll down to see the full summary -
Cuando la fuerza de fricción estática se convierte en fuerza de fricción cinética y viceversa
Abstract:The demonstration experiment here presented illustrates the behavior of static and kinetic friction forces on the sliding motion of a rigid body. It is also illustrated that these forces are not constant, in general. The objectives are satisfactorily gotten using a bar or an object which has a straight part, as a broom. The bar is placed horizontally on the index fingers; the fingers are sliced until they meet beneath the center of mass or they separate until one of them reach one end of the bar. When the fingers are brought together the bar slides alternately over only one finger; however, when they are separated, the sliding motion of the bar is produced without the alternation.⬇️ Scroll down to see the full summary -
Colisión en dirección vertical
Abstract:The demonstration experiment here presented illustrates a situation where the conservation laws of linear momentum and mechanical energy are not satisfied; however, their use allows a good qualitative description of the result observed. The objective is satisfactorily gotten by the analysis of the vertical collision between two balls. The balls with the appropriate masses are dropped, the small mass resting on top of the larger mass; after the collision between the bottom ball and the floor this ball does not have vertical motion, whereas the top ball rebounds up to a height higher than its original height.⬇️ Scroll down to see the full summary -
Approximation expressions for the large-angle period of a simple pendulum revisited
Abstract:This paper presents the experimental accuracy performance of each of the approximation expressions relative to the exact period for large amplitudes of a simple pendulum in the interval 0$^\circ$ $ \le \theta \le $ 180$^\circ$. The plots of the linearized exact period as a function of linearized formulae were carried out and relative errors in these expressions were investigated. In addition, this paper gives a clear idea how each formula approximates the exact period.⬇️ Scroll down to see the full summary -
Choque inelástico entre dos partículas: análisis basado en el coeficiente de restitución
Abstract:An inelastic collision between two particles is treated using the restitution coefficient. Its geometrical interpretation is given, and the advantages of this new formulation are shown.⬇️ Scroll down to see the full summary -
On the need to enhance physical insight via mathematical reasoning
Abstract:It is becoming common to hear teaching advice about spending more time on the ``physics of the problem" so that students will get more physical insight and develop a stronger intuition that can be very helpful when thinking about physics problems. Based on this type of justification, mathematical skills such as the ability to compute moments of inertia, center of mass, or gravitational fields from mass distributions, and electrical fields from charge distributions are considered ``distracting mathematics" and therefore receive less attention. Based on published cited research on the subject, we'll argue a) that this approach can have a negative influence on student reasoning when dealing with questions of rotational dynamics, a highly non-intuitive subject where even instructors may fail to provide correct answers, and b) that exposure of students to mathematical reasoning and to a wide range of computational techniques to obtain the moment of inertia of different mass distributions will make students more comfortable with the subject of rotational dynamics, thus improving their physical insight on the topic.⬇️ Scroll down to see the full summary -
Brownian motion in a magnetic field and in the presence of additional external forces
Abstract:Our purpose in this paper is to solve exactly the Fokker-Planck-Kramers equation of a charged particle (heavy-ion) embedded in a fluid and under the influence of mechanical and electromagnetic forces. In this work the magnetic field is assumed to be constant and pointing along any direction of a Cartesian reference frame; the mechanical and electrical forces are both space-independent, but in general time-dependent. Our proposal relies upon two transformations of the Langevin equation associated with the charged particle's phase-space $( r, u)$. The first one is a fixed rotation which transforms the $( r, u)$-coordinates into other $( r^{\prime}, u^{\prime})$-coordinates, and makes it possible to re-orientate the magnetic field along an appropriate direction (say along the $z^{\prime}$-axis). The second one is a time-dependent rotation which transforms the $( r^{\prime}, u^{\prime})$-coordinates into other $( r^{\prime\prime}, u^{\prime\prime})$-coordinates, in which the resulting Langevin equation strongly resembles that of ordinary Brownian motion in the presence of external forces. Under these circumstances, the Fokker-Planck-Kramers equation can immediately be solved in the $( r^{\prime\prime}, u^{\prime\prime})$ phase-space, following our methodology developed in Ref. [Phys. Rev. E 76 (2007) 021106].⬇️ Scroll down to see the full summary -
Un comentario sobre el artículo: ``Tiempo mínimo y trayectoria de movimiento''
Abstract:The paper of V. Aboites and A. Pisarchik [1] show experimentals results interesting on the optimals movement trajectories by a group of students the treat of reach an object inside a pool. However, in spite of that your theorics and experimentals conclusion are very likes, the statisticals estimation corresponding to the experimental out line necesited of some amendments. \end{abstract} \keys{ Least action principle; minimum time principle. } \pacs{45.20.-d; 45.10.Db; 01.40.gb; 01.50.My; 01.80.+b } \begin{multicols}{2} \noindent En el artículo de reciente publicación: ``Tiempo mínimo y trayectoria de movimiento'' [1], los autores se plantean la veracidad del principio de mínima acción [2,3] en el sentido de que si los objetos inanimados eligen trayectorias obedeciendo tal principio, los humanos podrían también realizar acciones de movimiento que satisfagan ese mismo principio. Para lograr ese objetivo los autores del mencionado artículo plantean el siguiente problema: Se coloca un objeto sobre el agua en uno de los vértices de una alberca olímpica (50$\times$25 m). Posteriormente, desde un vértice opuesto de la alberca se hace correr por separado a un grupo de estudiantes para después saltar al agua y llegar hasta donde se encuentra tal objeto. En este planteamiento, los desplazamientos por tierra y por agua representan mediciones por separado de cada uno de los estudiantes. Por lo tanto, lo que los autores desean averiguar aquí es si los estudiantes en su trayectoria elegirán la que los conduzca al objeto en un tiempo mínimo. Al modelar esquemáticamente el planteamiento del problema, los autores encuentran una expresión que describe el tiempo de desplazamiento de los estudiantes tanto por tierra como por agua [Ec. (5) en su artículo en función de la posición $y$ (ver Fig. 1 en Ref. 1) que elegirán los estudiantes para saltar al agua]. Esta misma expresión contiene también los parámetros velocidad promedio sobre la tierra ($v_{t}$) y dentro del agua ($v_{a}$). En Ref. 1 los autores tabulan los resultados de las mediciones de los tiempos empleados y las correspondientes velocidades, tanto por tierra como por agua. Al realizar las estimaciones estadísticas correspondientes a estas mediciones (desviación estándar y error absoluto), los autores obtienen órdenes de magnitud equivocados. Para la velocidad promedio por tierra $v_{t}$ ellos obtienen una desviación estándar $\sigma_{v_{t}}= 0.00727$ y un error absoluto $\Delta E_{v_{t}} \approx 0.0902 $. Pero al reproducir estos cálculos encuentro que la desviación estándar $\sigma_{v_{t}}= 0.0809$, es decir, un orden de magnitud más grande que la obtenida por ellos en su artículo y el error absoluto $\Delta E_{v_{t}}\approx 0.1204$, también con un orden de magnitud más grande. Algo similar ocurre con las estimaciones estadísticas correspondientes a $v_{a}$. Ellos obtienen una desviación estándar $\sigma_{v_{a}}= 0.00032$ y un error absoluto $\Delta E_{v_{a}}\approx 0.005$, pero de igual forma, al reproducir estas estimaciones obtengo que $\sigma_{v_{a}}= 0.0170$, dos ordenes de magnitud más grande que la obtenida por ellos. Mientras que el error absoluto que obtengo es $\Delta E_{v_{a}}\approx 0.0177$, el cual es un orden de magnitud más grande que el obtenido por ellos. Finalmente, los autores, al hacer las estimaciones estadísticas correspondientes a la posición $y$ que los estudiantes eligen para saltar al agua, obtienen una desviación estándar $\sigma_{y}= 0.003$ y un error absoluto $\Delta E_{y}\approx 0.05$. Respecto a estas últimas estimaciones yo obtengo una desviación estándar $\sigma_{y}= 0.0556$, es decir, un orden de magnitud mayor que la obtenida por ellos. Mientras que el error absoluto que obtengo es $\Delta E_{y}\approx 0.0743$, el cual no varía mucho. Durante el proceso que se lleva a cabo para diseñar un experimento es recalcadamente importante tomar en cuenta la teoría de errores, tal y como se muestra en Ref. 4. En ese artículo, el autor muestra que la teoría de errores puede ser una muy útil herramienta para el diseño más eficiente de un experimento. Consecuentemente, los autores en Ref.~1 posiblemente necesitarán reconsiderar las técnicas de medición empleadas para el desarrollo de su experimento, para que así puedan obtener una mejor calidad experimental. \end{multicols} \medline \begin{multicols}{2} \begin{thebibliography}{99} %\bibitem{c1} \bibitem{Ab} V. Aboites y A. Pisarchik, \emph{Rev. Mex. Fís. E} 53 (2007) 52. \bibitem{Go} H. Goldstein, \emph{Classical Mechanics} (Addison Wesley, 1965). \bibitem{Ne} D.E. Neuenschwander, E.F. Taylor y S. Tuleja, \emph{The Physics Teacher} 44 (2006) 146. \bibitem{Ha} J.L. Haza, \emph{Rev. Mex. Fís. E} 49 (2003) 57. \end{thebibliography} \end{multicols} \end{document} %Numero de paginas en dvi = \documentclass[spanish]{rmf-e} \usepackage{nopageno,rmfbib,multicol,times,epsf,amsmath,amssymb,cite} \usepackage[latin1]{inputenc} \usepackage{babel} \usepackage[]{caption2} \usepackage{graphics} % \spanishdecimal{.} \def\rmfcornisa{COMENTARIOS \hfill\rmf 54 (1) 87--88 \hfill JUNIO 2008} \newcommand{\ssc}{\scriptscriptstyle} % \def\rmfcintilla{ Rev. Mex. Fís.\/ 54 (1) (2008) 87--88} \clearpage \rmfcaptionstyle \pagestyle{myheadings} \setcounter{page}{87} \markboth{V. Aboites y A. Pisarchik} {Sobre: ``Un comentario sobre el artículo: Tiempo mínimo y trayectoria de movimiento''} \begin{document} \title{Sobre: ``Un comentario sobre el artículo: Tiempo mínimo y trayectoria de movimiento'' } \author{V. Aboites y A. Pisarchik } \address{Centro de Investigaciones en Óptica, Loma del Bosque 115 Col. Campestre León, 37150 Gto. } \maketitle \recibido{7 de diciembre de 2007}{13 de diciembre de 2007 } \begin{resumen} Se corrigen los valores de la desviación estándar y error absoluto reportados en los artículos ``Tiempo mínimo y trayectoria de movimiento'' [1] y ``Un comentario sobre el artículo: Tiempo mínimo y trayectoria de movimiento''[2]. \end{resumen} \descript{Mínima acción; tiempo mínimo. } \begin{abstract} The standard deviation and absolute error found in ``Tiempo mínimo y trayectoria de movimiento'' [1] and in ``Un comentario sobre el artículo: Tiempo mínimo y trayectoria de movimiento'' [2] are corrected.⬇️ Scroll down to see the full summary -
Sobre: "Un comentario sobre el artículo: Tiempo mínimo y trayectoria de movimiento"
Abstract:The standard deviation and absolute error found in ``Tiempo mínimo y trayectoria de movimiento'' [1] and in ``Un comentario sobre el artículo: Tiempo mínimo y trayectoria de movimiento'' [2] are corrected.⬇️ Scroll down to see the full summary
