We make a multicontextual and critical review of widely used undergraduate physics textbooks, regarding Pascal’s principle, and compare them with the original work of Blaise Pascal. Our analysis shows that there are inconsistencies throughout almost all the books considered, both conceptual and historical. We provide suggestions on how to overcome or fix these inconsistencies, so Pascal’s principle

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schrödinger equations with additional constraints. In fact, the method is general and can solve constrained minimization problems in many fields. We present the method for introductory applications in quantum mechanics including three qualitative

The one-dimensional (1D) hydrogen atom with potential energy V ( q ) = − e 2 /| q |, with e the electron charge and q its position coordinate, has been a source of discussion and controversy for more than 55 years. A number of incorrect claims have been made about its spectrum; for example, that its ground state has infinite binding energy, that bound states associated with a continuum of negative

The infinite square wall model is one of the simplest models to have been introduced in quantum mechanics. We employ this model to illustrate the quantum transitions of particles due to the deconfinement process. With the infinite square wall, we propose that a shift of the wall to a larger x position corresponds to the process of deconfinement with strong interaction. Two limits of the wall’s movement

It is often said, in connection with the Pauli principle of quantum mechanics, that ‘if the spatial wavefunction is symmetric under a coordinate swap, the particles huddle together; if antisymmetric, they spread apart’. While this saying is often true, this essay uncovers a counterexample.

We revisit the concept of optical spatial coherence by considering the case of the complex degree of spatial coherence induced over a plane by a quasi-monochromatic irradiating source. We apply the Van Cittert–Zernike theorem and exploit a Lloyd’s two-beam interferometer setup with its two small coherent light sources, as a way to illustrate the calculation of such complex spatial coherence, and because

We investigate generic heat engines and refrigerators operating between two heat reservoirs, for the condition when their efficiencies are equal to each other. It is shown that the corresponding value of efficiency is given as the inverse of the generalized golden mean, ϕ p , where the parameter p depends on the degrees of irreversibility of both engine and refrigerator. The reversible case ( p = 1)

The effects of speed humps and bumps in slowing vehicles were investigated using a mass suspended on a spring. An impulse was applied to the mass by lowering and raising the top end of the spring by hand. The impulse duration was varied to simulate different driving speeds, and the displacement of the mass vs time was recorded with a video camera. Maximum displacement of the mass was observed when

The launch in 2019 of the new international system of units is an opportunity to highlight the key role that the fundamental laws of physics and chemistry play in our lives and in all the processes of basic research, industry and commerce. The main objective of these notes is to present the new SI in an accessible way for a wide audience. After reviewing the fundamental constants of nature and its

The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of a Kronecker product and what we have termed the ‘bra-flipper’ operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac’s bra-ket notation. For the purpose of illustrating

Molecules and atoms that are normally gaseous at room temperature and pressure will liquefy or solidify as their temperature reduces or their pressure increases. In the apparatus detailed here a commercial cell contains pressurized SF 6 so that it exists in both gaseous and liquid states, with the density of both being similar at room temperature. The critical point on the phase diagram can then be

Analysis of institutional data for physics majors showing predictive relationships between required mathematics and physics courses in various years is important for contemplating how the courses build on each other and whether there is need to make changes to the curriculum for the majors to strengthen these relationships. We used 15 years of institutional data at a US-based large research university

This paper outlines some of the benefits of using virtual reality (VR) in physics education at the university level. Based on the existing experimental infrastructure of the low-background gamma spectroscopy laboratory, a VR experiment has been designed which includes all the stages of the physical measurement process. Following the VR experiment, the students receive pre-prepared experimental data

The mechanically controllable break junction (MCBJ) experimental setup is one of the main techniques employed in the study of electronic transport properties at the atomic and molecular scales. This work presents the construction of an inexpensive and simple but robust setup that shows the emergence of conductance quantization as a macroscopic gold wire is pulled to atomic dimensions. The homemade

We derive here, from first principles, the energy–momentum density of a perfect fluid in the form of an ideal molecular gas, in an inertial frame where the fluid possesses a bulk motion. We begin from the simple expressions for the energy density and pressure of a perfect fluid in the rest frame of the fluid, where the fluid constituents (gas molecules) may possess a random motion, but no bulk motion

We discuss the influence of two factors on the deviations from the model of the magnetic field of a long straight wire. Firstly, we derive the magnetostatic analogue of McCullagh’s formula for the case of the infinitely long straight conductor with an arbitrary cross-section. Using this equation on the basis of its practical significance, we find that the greatest deviations from the long straight

Here we study the physical problem in which a thin bar, such as a strip of paper, is bent under several types of loads and boundary conditions. Initially, we consider lengthwise compression of the strip due to concentrated forces applied on its ends. We present this problem for the three boundary conditions: doubly-clamped, hinged–clamped, and doubly-hinged ends constrained on a flat surface. We also

We present a simple red blood cell (RBC) model and solve it only based on the variational method. Such a model allows us to obtain the morphological characteristics of human mature RBC under normal conditions, and to study its shape transformation induced by osmotic pressure. This study requires only modest computational capabilities and geometric knowledge and thus is well suited to be a part of an

The paper explores the shadow of the repulsive Rutherford scattering—the portion of space entirely shielded from admitting any particle trajectory. The geometric properties of the projectile shadow are analyzed in detail in the fixed-target frame as well as in the center-of-mass frame, where both the charged projectile and the charged target cast their own respective shadows. In both frames the shadow

Exact flows are calculated for an infinite set of pipe cross-sections, each with variable corrugations, ranging from angular to smooth as a parameter varies. The results are compared with three ‘rules of thumb’ which give general but approximate formulae for the rate of flow through a pipe of given cross-sectional shape. These are (i) the Saint-Venant formula, in which the flow is related to the area

We present a kinesthetic active learning activity, based on tug-of-war, that challenges upper secondary education and undergraduate learners to engage with Newton’s laws. The learning module has two parts. In the first part students analyse the game using common introductory physics concepts. They use those insights to make predictions about what factors affect the outcome of the game. In the experimental

This article looks at the qualitative survey responses of LGBT physicists about their experiences of exclusionary behavior and harassment. Of the 324 respondents 71 reported such an experience and gave a qualitative response. Findings indicate that the majority of respondents experienced exclusionary behavior based on their gender expression or being a woman. The behavior came mostly in the forms of

Recent progress in the development of quantum technologies, most notably in the context of quantum computing and cryptography, poses the question of whether and how to teach the modern and sophisticated underlying theory of quantum physics, and its applications, at school. To this end, we present a game-based approach to teach Bell inequalities and quantum cryptography at undergraduate level. The approach

We have developed a compact modular rotating-analyzer ellipsometer (RAE) with a spectrum range of 200–850 nm. Spectroscopic ellipsometry is a non-destructive characterization based on an optical method. It is used widely to obtain the dielectric constant, thickness, and surface roughness of thin films. Our homemade RAE comprises standard modular components that are available on the market, such as

It is common for senior physics students at many universities to perform optical pumping experiments using a rubidium cell in an integrated apparatus. Such experiments provide an encounter with atomic structure in the context of a standard technique of modern atomic physics. Typically, students investigate radiofrequency resonances between Zeeman levels and measure hyperfine splitting. Despite its

The equation of motion of an object in a rotational frame is often confused with the equation of motion described by the polar coordinates in an inertial system, as demonstrated in a previous article (2008 Eur. J. Phys. 29 599–606). In this paper, explanations are supplemented to some misleading statements regarding the mechanical motion in rotating frames, and some additional descriptions regarding

A mass attached to a spring can be set in motion by applying a force either to the mass or the spring. We consider a problem where a short impulse is applied to the spring in an attempt to project the mass at maximum speed. The problem arises when swinging a flexible golf club or a fishing rod, both of which vibrate at low frequency as a mass–spring system. It is shown that maximum speed of the mass

A Newton’s cradle experiment is described where the end ‘ball’ was much heavier than the rest and acted as an end stop. The experiment was conducted to examine the elastic response of billiard balls to a measured impact force, as well as the behaviour of a billiard ball chain in a cradle. The results agree well with a Hertzian force law and are qualitatively similar to those for a conventional cradle

A length of chain rotating about a vertical axis, fixed only at the pivot, adopts a shape that is defined by the number of nodes. The maximum number of nodes is determined by rotation frequency. To date no exact or approximate analytical solutions have been found except for the linearized case (small angles). In this paper angular solutions are determined for the nonlinear helicoseir rotating at high

The article ‘Comment on “A note on Purcell’s basic explanation of magnetic forces”’ (2020 Eur. J. Phys. 41 068001) disputes the validity of the results presented in D’Abramo (2020 Eur. J. Phys. 41 025203). In this reply, we provide several arguments against that criticism and confirm the original conclusions.

In his seminal book on electromagnetism, Purcell presented a conceptually rich discussion in which he used Lorentz contraction to relate the electromagnetic fields of a current-carrying wire when observed from different inertial frames. In a recent paper D’Abramo (2020 Eur . J . Phys . 41 025203) argued that Purcell’s approach has a very limited validity and when it is applied in examples slightly

A portable, low-cost, all-in-one biopotential monitoring system that can be used for demonstrating the basic characteristics of electrical activities of the human brain and body for undergraduate physics students is described. The monitoring system consists of a wireless biopotential amplifier, an electrode cap and a software interface. Some of the biopotential activities recorded from the monitoring

When a massive test particle or a photon fall radially into a black hole, their energy, as measured by a static observer located very close to the horizon, diverges. In introductory courses on general relativity, this fact gives rise to questions about the reality of this divergence and its eventual effect on the geometry of the black hole. We address these concerns and show that, eventually, it is

Grading can shape students’ learning and encourage use of effective problem solving practices. Teaching assistants (TAs) are often responsible for grading student solutions and providing feedback, thus, their perceptions of grading may impact grading practices in the physics classroom. Understanding TAs’ perceptions of grading is instrumental for curriculum developers as well as professional development

We describe gauge symmetry at the elementary level aiming at undergraduate and first-year graduate theoretical physics students. The formal definition of gauge invariance as a local symmetry of the action is given and further elaborated and interpreted in detail in two physical models, namely, a mechanical system and the prototypical gauge field theory of electrodynamics. The first model, consisting

The double slit experiment was the first demonstrative proof of the wave nature of light. It was expounded by the English physician-physicist Thomas Young in 1801 and it soon helped lay to rest the then raging Newton–Huygens debate on whether light consisted of a fast-moving stream of particles or a train of progressive waves in the ether medium. In the experiment, light is made to pass through two

The teaching of basic circuits in early undergraduate physics courses is widespread and, to some extent, quite uniform. In most textbooks, the introduction of resistors, capacitors and inductors is followed by their assemblage into larger systems, together with mathematical calculations of charges and currents as functions of time. In this process, spatial features of circuits tend to be omitted. Here

In this article, we present the development and treatment of an inverse problem applied to data from the Felix Baumgartner stratospheric jump. This jump is well documented with a lot of data. Therefore, it makes a particularly well-suited example for teaching in a numerical techniques laboratory. The major aim of the article is to give guidelines in order to construct a simple, but not simplistic,

This paper presents an educational concept for promoting quantum teaching and learning via an educational structured quantum optical experiment. The experiment is designed to demonstrate the striking differences between classical physics and quantum physics, for example quantum interference of unbreakable photons (the ability of probabilities to interfere due to a phase sensitive superposition of states)

Harmonic motion is a significant topic in undergraduate lectures for university physics students. A typical example, presented in lectures around the globe, is the motion of a mass at the end of a spring. It should be emphasized that the harmonic motion in the aforementioned case is just an approximation for small displacements. However, the value of this example for teaching purposes is undeniable

An introduction to the Zwanzig–Mori–Götze–Wölfle memory function formalism (or generalized Drude formalism) is presented. This formalism is used extensively in analyzing the experimentally obtained optical conductivity of strongly correlated systems such as cuprates and iron-based superconductors. For a broader perspective both the generalized Langevin equation approach and the projection operator

The Markov chain Monte Carlo (MCMC) method is used to evaluate the imaginary-time path integral of a quantum oscillator with a potential that includes a quadratic term and a quartic term whose coupling is varied by several orders of magnitude. This path integral is discretized on a time lattice on which calculations for the energy and probability density of the ground state and energies of the first

This comment examines an article that develops a counterclockwise reversible Stirling cycle whose coefficient of performance equals that of a Carnot refrigerator. Unfortunately, among other issues, the proposed cycle is never in thermodynamic equilibrium and thus cannot match an idealized reversible Carnot.

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A solar thermal experiment for the thermal performance evaluation of parabolic dish solar cookers suitable for developing countries is presented. Three different solar cooking pots are compared experimentally using three different cooking fluids, namely water, sunflower oil and olive oil. The heating experiments are carried using three identical parabolic dish solar cookers. The mass of the fluid load

We describe in detail a high-performance project devised for outstanding undergraduate students with appropriate abilities in physical reasoning (rather than with a good standard preparation), centered around the well-known historical case of Newton’s theory of light and colours. The different action lines along which the project is developed are aimed at involving the students in: (1) thinking as

The effects of various types of damping on the period of the nonlinear pendulum are compared with experiment for oscillations of amplitude up to ∼180°. The factors affecting a comparison of experimental results obtainable with modern MEMs gyro/accelerometers with theory, namely a precise knowledge of the pendulum fundamental frequency ω 0 , the instrument calibration and the definition of the amplitude

In this paper, an algebraic solution for the bound states of the relativistic hydrogen atom is presented. The method discussed here adds an operator associated with the phase of the energy eigenstates to the set of variables of the problem. In terms of this set, appropriate ladder operators are constructed in order to express the full solution of the Dirac hydrogen equation. These ladder operators

Columns of water in inverted containers, such as upside-down glasses of water, are classic phenomena that demonstrate the effects of atmospheric pressure. This paper presents an analytical method to explore the role of liquid bridges and the associated capillary forces in the equilibrium condition and the criticality of water columns held in inverted containers by a cover sheet. This method has been

A thermometer is a temperature proxy, usually with a fixed number of parameters. When a nearly ideal gas or a similarly simple system is not available, the determination of a temperature scale is difficult, and has been subject to debate. Entropy uniqueness, due to Clausius, provides a fundamental theoretical criterion to answer this question. By measuring the heat flow d Q around a grid in p – V space

Measurements are presented of the drag force on several different balls falling vertically through water in a fish tank, at speeds up to 4.5 m s −1 . Experiments of this type are usually undertaken in a student laboratory by measuring the terminal velocity of an object falling either through air or a viscous liquid. At speeds slightly higher than the terminal velocity, additional effects can be observed

The International Physicists’ Tournament (IPT) 2019 dealt with 17 challenging problems. In this article, we present experimental as well as theoretical approaches as examples of one of these tasks. A ball placed on a hard and flat surface can oscillate when being hit by a jet of water from above. To explain the oscillations, a theoretical model is introduced and its predictions are compared to experimental

We have designed and fabricated an inexpensive AC susceptometer which works around room temperature. The susceptometer uses the principle of a mutual inductance bridge with a null detection algorithm. The bridge was balanced by two digitally controlled stepper motors coupled with two highly linear potentiometers. The susceptometer was tested with double-perovskite structured samples with transition

We consider the Thomas–Wigner rotation of coordinate systems under successive Lorentz transformations of inertial reference frames, and disclose its physical mechanism on the basis of the relativistic contraction of moving scale, and the relativity of the simultaneity of events for different inertial observers. This result allows us to better understand the physical meaning of the Thomas precession

We address an interesting problem in elementary quantum mechanics, namely how can one obtain the momentum state eigenfunctions for the infinite square well potential as a direct solution of the time-independent Schrödinger equation in momentum space. The conventional method for obtaining the momentum state eigenfunctions for the infinite square well potential is to take the Fourier transform of the

The quantum anharmonic oscillator has been solved numerically using matrix diagonalization technique. The interaction potential consisting of quadratic ( ##IMG## [http://ej.iop.org/images/0143-0807/41/5/055402/ejpab988cieqn1.gif] {$\frac{1}{2}k{x}^{2}$} ) and quartic ( λx 4 ) terms is embedded within an infinite square well potential of appropriate width, ‘ a ’ and its sine eigen functions are used

Composites based on candle wax and pencil graphite were fabricated with different concentrations of graphite in the range 0% w/w to 70% w/w. These composites were fabricated (‘ironed’) into a sandwich structure with kitchen aluminum foil serving as electrodes. The composites’ electrical resistance was measured and it was found that the composite with 15% w/w of graphite was the best choice for further

In their famous 1939 paper on the physics of nuclear fission, Niels Bohr and John Wheeler presented an eye-catching graph of the fission barrier energy for various nuclides. In this paper I develop a simplified approach to developing this graph which is both sensibly true to their analysis and appropriate for a student audience.

A simple experiment based on thermal imaging is devised to observe and measure, along a cooling fin in contact with a hot spot, the temperature profile determined by conductive and convective heat transport. By using a simple theoretical approach, the cooling fin equation is justified and applied to describe, in an educational framework and perspective, the experimental results. Both the experimental

Several natural phenomena are ruled by the same first-order differential equation. Curiously, the Friedmann equation of relativistic cosmology is of the same form, allowing for useful analogies to be built. Several applications of this equation to phenomena occurring in nature are presented.