Catálogo de publicaciones - revistas

<jats:p>We review an explicit approach to obtaining numerical solutions of the Schrödinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with several examples. Because of its explicit nature, the algorithm can be readily extended to systems with a higher number of spatial dimensions. We show that the method also generalizes the staggered-time approach of Visscher and allows for the accurate calculation of the real and imaginary parts of the wave function separately.</jats:p>

<jats:p>We analyze a variety of Gaussian integrals with the aim of revisiting the derivation of the Hubbard–Stratonovich transformation as given in standard graduate-level textbooks and provide an overview of its applications. We pinpoint problematic steps in the usual discussions and propose careful derivations of the Hubbard–Stratonovich identity pertinent to a variety of situations relevant to statistical physics and quantum field theory. These derivations are based on direct use of either a resolution identity or a series expansion. A few homework problems for students are suggested.</jats:p>

<jats:p>One of the most accurate ways to measure the impedance of an electrical component is to place it in a bridge that is then balanced. The most familiar bridge in an undergraduate laboratory is the Wheatstone bridge, which can measure resistance to high precision. Other types are, however, required for reactive components. This paper describes the use of Anderson's bridge to measure inductance, allowing both the inductance and resistance of different inductors to be determined. The inductors are analysed with different cores: perspex, copper, and steel. Models for the inductance that include the effect of skin depth, winding proximity, eddy currents, and core effects are introduced and compared to measurements in the frequency range from 100 Hz to 100 kHz.</jats:p>

<jats:p>The coefficient of sliding friction is usually regarded as a constant for any given surfaces although it is sometimes known to vary with sliding speed. An experiment is described where the coefficient of friction for a billiard ball decreases to a very small value as the sliding speed decreases to zero, after which the ball starts rolling without sliding. A simple theoretical explanation is provided.</jats:p>

<jats:p>The first global e-competition on astronomy and astrophysics was held online in September–October 2020 as a replacement for the International Olympiad on Astronomy and Astrophysics, which was postponed due to the COVID-19 pandemic. Despite the short time available for organization, 8 weeks, the competition was run successfully, with 325 students from over 42 countries participating with no major issues. The feedback from the participants was positive and reflects the ways in which such events can boost interest in astronomy and astronomy education. With online activities set to become more prevalent in the future, we present an overview of the competition process, the challenges faced, and some of the lessons learned, aiming to contribute to the development of best practices for organizing online competitions.</jats:p>

<jats:p>The Wilberforce pendulum illustrates important properties of coupled oscillators including normal modes and beat phenomena. When helical spring is attached to a mass to create the Wilberforce pendulum, the longitudinal and torsional oscillations are coupled. A Wilberforce can be constructed simply from a standard laboratory spring, and a smartphone's accelerometer and gyroscope can be used to monitor the oscillations. We show that the resulting time-series data match theoretical predictions, and we share the procedures for observing both normal modes and beats.</jats:p>

<jats:p>Oblique angle collisions between two balls or two disks have been addressed by many authors. This paper describes oblique angle collisions between three or four billiard balls. Measurements and calculations are presented for cases where one ball is incident obliquely on two or three identical balls, which are in contact and initially at rest. Conservation laws alone are not sufficient to predict the outcome. Adding information about the impact forces on each ball (and ignoring friction forces) provides good theoretical agreement with experimental results.</jats:p>

<jats:p>The Landau–Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational effort, but has a number of complex numerical and algorithmic issues that can be resolved through dedicated work. It can be used to teach computational concepts, such as accuracy, discretization, and extrapolation, and it reinforces quantum concepts of time-evolution via a time-ordered product and of extrapolation to infinite time via time-dependent perturbation theory. In addition, we discuss the concept of compression algorithms, which are employed in many advanced quantum computing strategies, and easy to illustrate with the Landau–Zener problem.</jats:p>