Potenciais singulares na equação de Schrodinger unidimensional via transformada de Laplace

The present work has as its goal to treat well known and interesting unidimensional cases from quantum mechanics through an unusual approach within this eld of physics. The operational method of Laplace transform, in spite of its use by Erwin Schrödinger in 1926 when treating the radial equation for the hydrogen atom, turned out to be forgotten for decades. However, the method has gained attention again for its use as a powerful tool from mathematical physics applied to the quantum mechanics, appearing in recent works. The method is specially suitable to the approach of cases where we have potential functions with even parity, because this implies in eigenfunctions with de ned parity, and since the domain of this transform ranges from 0 to ∞, it su ces that we nd the eigenfunction in the positive semi axis and, with the boundary conditions imposed over the eigenfunction at the origin plus the continuity (discontinuity) of the eigenfunction and its derivative, we make the odd, even or both parity extensions so we can get the eigenfunction along all the axis. Factoring the eigenfunction behavior at in nity and origin, we take the due care with the points that might bring us problems in the later steps of the solving process, thus we can manipulate the Schrödinger's Equation regardless of time, so that way we make it convenient to the application of Laplace transform. The Chapter 3 shows the methodology that must be followed in order to search for the solutions to each problem

Concepções de alunos do ensino médio sobre o tema água: subsídios para o planejamento de atividades investigativas interdisciplinares

Meaningful learning occurs when new knowledge to be aggregated are grounded in other students already possess. In preparing didactic sequences for teaching concepts, one should take into account these concepts and knowledge to produce more effective and lasting learning, and build new concepts that will become subsumes for subsequent learning. This research was developed in a subproject linked to institutional Scholarship Program Initiation to Teaching (PIBID) of a Universidade Estadual Paulista. The proposal is based on the articulation of the Public School and the University, strengthening the initial training of undergraduates, and continued teacher network, improving the quality of education. The proposed work is based on interdisciplinary research and teaching by investigation. Undergraduates in Biology, Physics, Mathematics and Chemistry jointly propose interdisciplinary teaching activities and investigative applied to high school students of Public School partner. To survey the views of these students on the theme Water, they were asked to draw up an essay entitled "The importance of water", with the aim of organizing information for planning a teaching strategy that articulates the disciplines of training of undergraduates. In this paper we present a qualitative analysis of these essays, performed based on content analysis. The analysis allowed to identify existing concepts in students' cognitive structure and classify them into adequate and inadequate compared to scientifically accepted concepts. Several misconceptions were raised indicating the need to produce didactic sequences that in addition to working the concepts presented in the curriculum of disciplines take into consideration the possibility of more meaningful learning. This research produced the elucidation of existing concepts, indicating where deficiencies were larger. One major contribution was the realization that concepts that may be considered by teachers as simple and already acquired by the students often come so misguided in their explanations. From the results obtained, integrated activities have been planned and implemented, and more relevant to the needs of students aiming to recover and enrich the knowledge they possessed, encouraging the use of scientific concepts and their application to daily living situations.

Guerra e o desenvolvimento científico: uma superaula interdisciplinar e investigativa construída em torno de um experimento central

This research presents the description of the assembly, development and execution of an experiment and of an interdisciplinary and student research activity built by some undergraduates from Biological Sciences, Physics, Mathematics and Chemistry PIBID subprojects of the Faculty of Science, FC - UNESP, Bauru/SP Campus. These subprojects are part of a single interdisciplinary group, which has as its main activity the Superclass, which consists of an intervention of the PIBID members during the class schedule, with an interdisciplinary and student research didactic sequence, applied by four groups of ten members, in two local State Schools. The experiment treated in this assignment was a miniature cannon (minicannon), and it was used in a Superclass that had the War and Science Development as its theme, wherein the knowledge of all areas were built from the analysis of the multiple variables involved on the cannon shots. These variables were surveyed with the students through the experiment research, during the Superclass, being focused on three of them: the shot and the explosives; the trajectory; and the target. The experiment was extremely successful, because it could instigate the students, who were interested, questioning and debaters for several times during the class. The minicannon made possible the interdisciplinary and the student research work among the four areas of science involved. Despite it has been a laborious experiment in its construction, it has proven to be innovative, and its use has transformed the students‟ ingenuous curiosity into epistemological curiosity, a key factor in the construction of scientific knowledge, wherein the dialogue established in the Superclass explored this new curiosity

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Completeness for coherent states in a magnetic-solenoid field

This paper completes our study of coherent states in the so-called magnetic-solenoid field (a collinear combination of a constant uniform magnetic field and Aharonov-Bohm solenoid field) presented in Bagrov et al (2010 J. Phys. A: Math. Theor. 43 354016, 2011 J. Phys. A: Math. Theor. 44 055301). Here, we succeeded in proving nontrivial completeness relations for non-relativistic and relativistic coherent states in such a field. In addition, we solve here the relevant Stieltjes moment problem and present a comparative analysis of our coherent states and the well-known, in the case of pure uniform magnetic field, Malkin-Man'ko coherent states.

Coherent states and related quantizations for unbounded motions

We discuss the construction of coherent states (CS) for systems with continuous spectra. First, we propose to adopt the Malkin-Manko approach, developed for systems with discrete spectra, to the case under consideration. Following this approach, we consider two examples, a free particle and a particle in a linear potential. Second, we generalize the approach of action-angle CS to systems with continuous spectra. In the first approach we start with a well-defined quantum formulation (canonical quantization) of a physical system and the construction of CS follows from such a quantization. In the second approach, the quantization procedure is inherent to the CS construction itself.

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q = 2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.

El vulcanismo holoceno de Gran Canaria: aplicación de un sistema de información geográfico

Programa de Doctorado, Física, Matemática, Geología y Clima.

Biestabilidad óptica: una panorámica

Entre las aportaciones más significativas que ha hecho la Electrónica Cuántica en los últimos años, dentro del campo de los dispositivos con uso potencial en diferentes terrenos, se encuentra, sin duda, el de la Biestabilidad Optica. Desde su planteamiento teórico por Szóke, en 1969, hasta la primera aparición de un elemento que ofreciese en el laboratorio propiedades experimentales concordantes con dicha teoría, pasaron exactamente seis años. Desde 1969, Szóke no ha vuelto a publicar ningún artículo en este campo, pero los investigadores que desde 1975 comenzaron a trabajar en él, lo han hecho hasta nuestros días con una ley prácticamente exponencial. Si se analizan con un cierto detalle, por otra parte, las tendencias previas de los diferentes grupos puede verse que, la mayor parte de ellos, provienen de ramas de la Electrónica Cuántica dedicados al estudio de fenómenos no-lineales de interacción radiación-materia. Pero hay también un número muy apreciable de otros grupos que habían estado trabajando en problemas de transiciones de fase en sistemas fuera del equilibrio, en física de materiales, tanto semiconductores como no semiconductores en física matemática y recientemente, en comunicaciones ópticas y en tecnología de ordenadores.

A gauge theory for continuous spin particles

In this dissertation we explore the features of a Gauge Field Theory formulation for continuous spin particles (CSP). To make our discussion as self-contained as possible, we begin by introducing all the basics of Group Theory - and representation theory - which are necessary to understand where the CSP come from. We then apply what we learn from Group Theory to the study of the Lorentz and Poincaré groups, to the point where we are able to construct the CSP representation. Finally, after a brief review of the Higher-Spin formalism, through the Schwinger-Fronsdal actions, we enter the realm of CSP Field Theory. We study and explore all the local symmetries of the CSP action, as well as all of the nuances associated with the introduction of an enlarged spacetime, which is used to formulate the CSP action. We end our discussion by showing that the physical contents of the CSP action are precisely what we expected them to be, in comparison to our Group Theoretical approach.

Sistemas integrables discretos, polinomios matriciales ortogonales y problemas de Riemann-Hilbert

El propósito de esta tesis doctoral es el estudio de la conexión, mediante el problema de Riemann-Hilbert, entre sistemas discretos y la teoría de polinomios matriciales ortogonales. La investigación de los modelos integrables se originó en la Mecánica Clásica, en relación a la resolución de las ecuaciones de Newton [2]. Los trabajos de Liouville, Hamilton, Jacobi y otros sentaron las bases de los sistemas integrables como prototipos modelos resolubles por cuadraturas, v.g., por integración directa [7]. Hay una cantidad importante de investigación dedicada a los aspectos geométricos de los sistemas clásicos integrables y superintegrables [66], [82], especialmente en relación a la separación de variables de la ecuación de Hamilton-Jacobi [75]. Fue la aplicación, en la segunda mitad del siglo pasado, de la transformada espectral inversa para la resolución del problema de Cauchy de la ecuación de Korteweg-de Vries [42, 43] la que marcó el inicio de una nueva etapa en este campo, el del estudio de sistemas integrables con un número infinito de grados de libertad, que generalmente se expresan en términos de jerarquías de ecuaciones no lineales en derivadas parciales. Particularmente reseñable, por su aplicación en la hidrodinámica y en la óptica cuántica, es la aparición de las soluciones a un número de solitones arbitrario. En las últimas tres décadas ha habido un importante interés por el estudio de modelos discretos, v.g., sistemas dinámicos de nidos en un retículo de puntos, y expresados en términos de ecuaciones no lineales en diferencia parciales. Muchas de las técnicas encontradas en el mundo continuo se extendieron a este nuevo contexto discreto. Hay dos razones fundamentales para este interés...

Lezioni elementari di fisica matematica /

contiene tom. I y tom. II.

POR UM ENSINO APRENDENTE: A FORMAÇÃO DE PROFESSORES DAS CIÊNCIAS NO SÉCULO XXI

A presente pesquisa investiga a formação de professores das ciências e sua perspectiva para o século XXI, a partir da análise das manifestações acadêmico-científicas de docentes doutores pesquisadores em educação científica nas áreas de Biologia, Química, Física, Matemática e Ciências da Natureza. Trata-se de uma pesquisa de natureza qualitativa, cuja narrativa procura contemplar aspectos de formação dessas áreas em meio aos conflitos, embates, especificidades e necessidades do atual contexto educacional. Busco tratar de visões e assumir posições sobre o que os professores das Ciências precisam aprender, pela configuração das tendências de formação e das práticas de ensino e de aprendizagem consideradas no século XX, bem como das projeções do que se põe como desejável para o século XXI. Nesse âmbito, identifico cinco categorias analíticas que são postas a partir de entrevistas junto aos meus sujeitos de pesquisa. Em relação à primeira categoria de pesquisa as tendências apontam que os conteúdos científicos são imprescindíveis, porém não suficientes durante o processo educativo, havendo necessidade de juntar o seu valor formativo. A segunda categoria traz a consideração do aluno no processo de aprender e ensinar ciências. Dentre o que não pode mais ser admissível neste século, a terceira categoria discute a dissociação entre ciência, tecnologia e sociedade atrelada a uma visão fragmentada de ciência. A quarta categoria aponta o que é posto de novidade na formação de professores das ciências, e a quinta categoria põe em discussão as necessidades formativas de professores das ciências para o século XXI. As análises dessas tendências em função dos relatos e entrevistas desses sujeitos de pesquisa são responsáveis pela integração entre o ensinar e o aprender, compartilhando os saberes pedagógicos, filosóficos, sociológicos, científicos. A partir da literatura atual sobre a formação de professores de ciências, procuro dar conta de algumas inquietações que permeiam a investigação e corroboram com uma mudança epistemológica do ensino: Quais aspectos devem ser prioritariamente considerados no âmbito da formação de professores das ciências? Quais as necessidades formativas desses professores? As contribuições acadêmicas a respeito dos saberes profissionais dos professores têm contribuído sobremaneira para o estabelecimento de uma cultura reflexiva em torno da prática docente de forma bastante crítica. Palavras-chave: 1. Formação de professores; 2. Ensino das ciências; 3. Necessidades formativas no século XXI.

Análisis vectorial y tensorial. Una aplicación a las ondas planas en sismología

El análisis tensorial tiene aplicaciones en el campo de la geometría diferencial de curvas y superficies en un espacio ordinario, así como la generalización a espacios de mayor dimensión o regularmente llamada geometría Rimaniana; otra aplicación es en la física matemática, en la cual, el análisis tensorial permite la formulación de las leyes naturales en términos de tensores los cuales son independientes de cualquier sistema coordenado en particular. Como los vectores son uno de los muchos tipos de tensores que hay, se dan conceptos básicos del análisis vectorial tales como: coordenadas cartesianas rectangulares, producto escalar y vectorial, diferenciación con respecto a una variable escalar y diferenciación parcial haciendo un desarrollo suciente del operador nabla. Se dan los principios fundamentales de los tensores los cuales son conceptos matemáticos o físicos que tienen ciertas leyes especícas que están relacionados con los cambios en el sistema coordenado y se llega hasta la ecuación de movimiento escrita en forma tensorial.