Catálogo de publicaciones - revistas

<jats:p>At first glance, a simple model of an RLC circuit taught in undergraduate courses provides a reasonable fit to experimental data. However, careful analysis demonstrates that this model does not accurately describe the behavior of the oscillations in this circuit and requires further refinement. Measuring and analyzing data from this system provides an opportunity for advanced lab students to engage in hypothesis construction, modeling, and experimental design as they seek to explain the discrepancy between these data and a model. The learning outcomes of this activity are consistent with the AAPT guidelines on the undergraduate laboratory experience. Furthermore, such experimentation allows students to bridge the gap between classroom learning and the real world.</jats:p>

<jats:p>We present several variations of a proof of the position-momentum uncertainty principle that are based on the calculus of variations and does not rely on the Cauchy–Schwartz inequality. We show that the stationary uncertainty wave functions are the Hermite–Gaussian solutions to the quantum harmonic oscillator problem, that the minimum uncertainty wave function is the Gaussian, and that stationary uncertainty wave functions must be their own Fourier transforms. We also provide a calculus of variations proof of the Cauchy–Schwartz inequality. Finally, we discuss the properties of wave functions that are their own Fourier transforms and provide examples of such functions that may be of interest to teachers of undergraduate and graduate level quantum mechanics courses.</jats:p>

<jats:p>We present a framework designed to illustrate the dynamics of a quantum particle tunneling from a bound state into a continuum of states under the influence of an external field. We concentrate on the question of what is the best classical-level description of the escaping particle. A toy model is constructed and investigated through complementary numerical, analytical, and approximate solutions. Issues related to the location of the apparent exit from the “quantum tunnel” are addressed in the language of Wigner trajectories and discussed in relation to the other types of solutions.</jats:p>

<jats:p>The normalization of scattering states is more than a rote step necessary to calculate expectation values. This normalization actually contains important information regarding the density of the scattering spectrum (along with useful details on the bound states). For many applications, this information is more useful than the wavefunctions themselves. In this paper, we show that this correspondence between scattering state normalization and the density of states is a consequence of the completeness relation, and we present formulas for calculating the density of states, which are applicable to certain potentials. We then apply these formulas to the delta function potential and the square well. We then illustrate how the density of states can be used to calculate the partition function for a system of two particles with a point-like (delta potential) interaction.</jats:p>

<jats:p>The paper presents a simple yet rigorous analysis of the transient of the spatial distribution of the kinetic energy of a classical ideal monoatomic dilute gas that passes from non-equilibrium to equilibrium. The proposed approach is event-based, in the sense that the evolution of the system is analyzed as a function of the random number of collisions in a given time interval. Taking a very simple yet realistic model of collision, the paper shows that collisions between atoms lead exponentially to energy equipartition.</jats:p>

<jats:p>We consider the motion of a frictionless piston that separates the surrounding atmosphere from an ideal gas enclosed within a cylinder, with no friction or viscous dissipation arising within the gas or surrounding atmosphere. Although no mechanically based dissipative mechanisms act, the motion of the piston is still damped if heat transfer between the gas and the piston occurs at a finite rate. Hence, as long as some kind of irreversibility develops within the system, such as irreversible heat transfer, the piston will not oscillate back-and-forth indefinitely and must eventually come to rest. We provide detailed thermodynamic and numerical analyses of this thermal damping, various aspects of which should prove useful to both students and instructors when discussing the first and second laws of thermodynamics.</jats:p>

<jats:p>In an advanced undergraduate instructional laboratory, it is often necessary to analyze the spectrum of light emitted from an experimental setup. There are numerous instruments that are used to accomplish this analysis, including spectrometers and spectrographs. In this report, we present 3D-printed, low-budget spectrographs (∼ US $200), which are specifically designed for different applications. For example, one can either observe a visible spectrum over a large range of wavelengths about a desired center wavelength or achieve more precise measurements by choosing a smaller part of the visible spectrum. Our generalized design approach is well within the knowledge base of advanced undergraduate physics majors and can be applied to a wide range of applications within the visible spectrum. To demonstrate the utility of these designer spectrographs, we provide examples of recording multiple doublets in the sodium spectrum (a determination of the fine structure spin-orbit splitting of the 3p energy level) as well as measuring the wavelength differences between the hydrogen and deuterium Balmer alpha lines (a measurement of an isotope shift).</jats:p>

<jats:p>We introduce a natural way of visualizing the entropy production in heat transfer processes between a system and a thermal reservoir. This representation highlights the asymmetric character of the heating and cooling processes when they are analyzed from the second-law perspective.</jats:p>