The Physics Educator

Numerous physical and chemical processes can be accurately described by first-order differential equations and can be solved through analytical methods. The solutions to these equations necessitate the specification of initial or boundary conditions. In the realm of physics and chemistry education, the ability to visualize the solutions of differential equations and comprehend their implications for physical/chemical changes holds significant importance. XCOS, an open-source software tool, serves as a valuable resource for both solving differential equations and graphically representing their solutions. Furthermore, XCOS aids in tackling nonlinear differential equations for which analytical solutions are often elusive. This paper delves into radioactive decay and decay series reactions by first-order differential equations. The paper explores the successful resolution and visualization of the phenomenon involving differential equations through XCOS. This approach extends to the manipulation of various parameters within the equations, further fostering inquiry-based learning.

If a Slinky suspended in a U-shape is rotated horizontally, it will have the shape of an upside-down $\mathrm{\Omega }$, like $\mathrm{\Omega }$, due to the centrifugal force in the horizontal direction acting on each point of the Slinky. In this paper, we discuss the shape of a rotating Slinky in both theoretical and experimental aspects. The rotating Slinky has the shape described by a multi-valued function if the angular velocity of the rotation satisfies $\omega >\pi \sqrt{K/M}$. Our theoretical results are in good agreement with experimental observations. The video of the experiments can be viewed at https://youtu.be/rpu9Ol2jdAM.

Periodic boundary conditions (PBCs) are a pivotal concept in the treatment of ideal lattices of infinite extent as a finite lattice. Most undergraduate texts that delve into the analytical treatment of lattice dynamics solve the problem in the reciprocal space with an implicit assumption of PBCs. While the traditional approach centered in the reciprocal or $k$-space is elegant for simple one-dimensional lattice structures, the method becomes mathematically cumbersome for more complex lattices with real-world applications, such as a honeycomb lattice involving a $4\times 4$ secular determinant.

In this work, we have explored the solution of lattice dynamics in direct space numerically, by constructing unit cells through an explicit implementation of Born–von Karman PBCs and solving the lattice dynamical equations in the displacement–time domain using the fourth-order Runge–Kutta algorithm. The Fast Fourier Transform technique is then used to obtain the phonon frequency spectrum corresponding to the computed instantaneous displacements. The fidelity of the model is validated by the agreement of the computational results obtained for the phonon spectrum at high symmetry points in the Brillouin zone with the analytical values for the given problem. Initially, the dynamics and the phonon spectrum are explored for monatomic and diatomic linear lattices which serve to act as introductory cases for the approach before investigating the 2D monatomic square and honeycomb lattices using the nearest and next-nearest neighbor approximations. A short-range force constant model employing the central forces and angular forces is used for the monatomic square lattice to account for the interatomic interactions. Our computational approach is expected to be physically more intuitive for a student for visualizing the periodicity of a given lattice and understanding its related dynamics. The approach demonstrates the usage of Born–von Karman PBCs in constructing a unit cell that effectively captures the dynamics of a lattice system, complementing the traditional secular determinant formalism. The work also illustrates an instance of how the computer programming can be used as a tool to empower the students to explore abstract concepts in physics. A honing of programming and computational skills of students enables them to interact with dynamic models in physics and gain deeper insight into the real-world applications of physics principles. Target group of this work is the students and educators at undergraduate level who seek a thorough and didactic comprehension of lattice dynamics.

We determine the acceleration due to gravity $(g)$ in a novel way using a magnetic sensor and video analysis technique of a smartphone. The same applications are used to measure the terminal velocity of a magnet falling through a conducting pipe and the magnetic moment of the magnet from its torsional oscillations. This experiment would appear to be intriguing, as it combines elements of magnetism, terminal velocity, and electromagnetic damping to determine $g$.

A Quantum Computing Concept Inventory is needed for the acceleration of uptake of best practice in quantum computing education required to support the quantum computing workforce for the next two decades. Eight experts in quantum computing, quantum communication or quantum sensing were interviewed to determine if there is substantial nonmathematical content to warrant such an inventory and determine a preliminary list of key concepts that should be included in such an inventory. Developing such an inventory is a challenging task requiring significant international ‘buy-in’ and creativity to produce jargon-free valid questions which are accessible to students who are yet to study quantum mechanics.