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Teaching quantum mechanics within a nature-of-science framework
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| Pengarang | : | Marco Giliberti; Luisa Lovisetti |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 2) |
| Halaman | : | 172-179 |
| Abstrak | : | We know from physics education research that, for effective physics teaching, knowledge needs to be framed within a context where the nature of science plays an essential role. This work presents the framework we have developed for introducing pre-service and in-service teachers to quantum mechanics via an active learning approach. It starts with some selected elements of the history of quantum mechanics, develops a set of physical principles, and then motivates constructing the formal aspects of quantum mechanics, such as states, linearity, superposition, observables, and probability. |
The spinorial ball: A macroscopic object of spin-1/2
| Pengarang | : | Samuel Bernard-Bernardet; Emily Dumas; Benjamin Apffel |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 2) |
| Halaman | : | 164-171 |
| Abstrak | : | In quantum physics lectures, half-integer spins are generally introduced as “objects that do not come back to their original state after one full turn but that do after two.” As a consequence, students often consider this behavior to be purely quantum mechanical. However, spin-1/2 is above all a geometrical property of the rotations group and can, therefore, also have practical consequences at the macroscopic scale. To illustrate this, we introduce and describe in this work a new pedagogical tool named the spinorial ball. It allows students to concretely manipulate a macroscopic 1/2-spin, which helps them to build intuition as to how the latter behaves under rotations. This object can also be used to introduce several general concepts from the theory of Lie groups, such as group homomorphism and homotopy classes of loops through the example of the groups SU(2) and SO(3). The spinorial ball provides a macroscopic visualization of all these concepts, which are ubiquitous in quantum physics. |
Beneath and beyond frustrated total reflection: A practical demonstration
| Pengarang | : | |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 2) |
| Halaman | : | 157-163 |
| Abstrak | : | Frustrated total internal reflection (FTIR) is analyzed from a novel perspective. Unlike similar works, the angle of incidence is used here as the experimental variable instead of the film thickness through which light tunnels. This method makes it possible to visualize not only the phenomenon of FTIR but also the resonance processes that occur for angles of incidence below the critical angle. An affordable straightforward experiment appropriate for undergraduates is presented. The experiment involves measuring the reflection and transmission of light through a pair of prisms separated by an air or water layer, and the results are in fair agreement with theory. |
Introducing key theoretical and data analysis tools in computational physics via Earth's temperature and climate
| Pengarang | : | David Syphers |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 2) |
| Halaman | : | 150-156 |
| Abstrak | : | This paper presents two thematically linked activities focused on temperature, climate, and climate change that can be used as engaging ways to introduce students to computational techniques. The first activity makes use of a non-equilibrium Earth undergoing climate change to introduce students to numerical solutions to differential equations via an ordinary first-order differential equation. This activity also introduces the concept of a toy model, and the important ideas of simulation validation and convergence. The second activity gives students several decades of local temperature data sampled hourly, introducing them to model fitting messy, real-world data, while also allowing them to see the effect of climate change. The amount of scaffolding for each activity is flexible, allowing instructors to adapt these activities to classes at advanced, intermediate, and even introductory levels. |
The most efficient thermodynamic cycle under general engine constraints
| Pengarang | : | Christopher Ong; Shaun Quek |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 2) |
| Halaman | : | 144-149 |
| Abstrak | : | Carnot's theorem guarantees the most efficient cycle to be the Carnot cycle provided that the state space is constrained between two isotherms. This paper considers what the most efficient cycle would instead be if the state space is constrained differently. We construct a general formalism for deriving the most efficient cycle in any constrained state space. We study the specific case of a rectangular domain on the ?−? space, and we prove that the Brayton and Otto cycles are the most efficient. |
A story with twists and turns: How to control the rotation of the notched stick
| Pengarang | : | Martin Luttmann; Michel Luttmann |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 2) |
| Halaman | : | 137-143 |
| Abstrak | : | The notched stick, also known as the Gee-Haw-Whammy-Diddle, is a wooden toy able to convert linear vibration into rotational motion, whose behavior has been intriguing both children and physicists for decades. The oldest scientific article one can find on this subject was published 87 years ago in the present journal. Here, we derive an analytical model of the system, supported by experimental results. We predict the direction of rotation and explain why the device is so easy to operate, even without fine control of the various parameters. The potential importance of the vertical displacement of the finger exerting the perturbation force is also highlighted. We finally discuss similarities between the mechanical system described here and the optical effect of birefringence. |
Ergodic Lagrangian dynamics in a superhero universe
| Pengarang | : | I. L. Tregillis; George R. R. Martin |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 2) |
| Halaman | : | 127-136 |
| Abstrak | : | We present a fictional scenario that, while undeniably whimsical, provides the foundation for a unique exercise in extended problem solving, physics analysis, and quantitative model development. Starting with the foundational premise of the Wild Cards shared-world superhero universe, we demonstrate how a variety of concepts appropriate to the advanced undergraduate level—ergodicity, functional analysis, Lagrangian mechanics, and the ever-important simplifying approximation—can be combined into a rich, coherent mathematical model. The goal of this case study is to develop a useful pedagogical exercise in exploring an open-ended research question that presents, at first glance, no clear path forward. Being both eclectic and lengthy, this exercise offers a unique way for students to apply their core physics and mathematics education. It is perhaps best used within a senior honors seminar or within a brief (e.g., January term) elective class. |
Testing the necessity of complex numbers in traditional quantum theory with quantum computers
| Pengarang | : | Jarrett L. Lancaster; Nicholas M. Palladino |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 1) |
| Halaman | : | 110-120 |
| Abstrak | : | A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory. The real-valued description is shown to predict correlations identical to those of complex-valued quantum mechanics for two types of Bell tests based on the Clauser–Horne–Shimony–Holt inequality. A slight modification to one test, however, results in different predictions for the real- and complex-valued constructions. While noisier devices are incapable of delivering convincing results, it is shown that certain devices possess sufficiently small error rates to falsify real-valued formulations of quantum theory for composite states. The results obtained with quantum computers are consistent with published experiments. This work demonstrates the feasibility of using freely available quantum devices to explore foundational features of quantum mechanics with minimal technical expertise. Accordingly, this treatment could inspire novel projects for undergraduate students taking a course on quantum mechanics. |
Simulating spin dynamics with quantum computers
| Pengarang | : | Jarrett L. Lancaster; D. Brysen Allen |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 1) |
| Halaman | : | 98-109 |
| Abstrak | : | IBM quantum computers are used to simulate the dynamics of small systems of interacting quantum spins. For time-independent systems with fewer than three spins, we compute the exact time evolution at arbitrary times and measure spin expectation values and energy. It is demonstrated that even in such small systems, one can observe the connection between conservation laws and symmetries in the model. Larger systems require approximating the time-evolution operator, and we investigate the case of ?=3 spins explicitly. While it is shown to be unfeasible to use such devices to probe such larger systems without more advanced algorithms or reliable error correction, we demonstrate that the quantum circuit simulator is an easy-to-use method for studying spin dynamics in systems with ?∼?(10) spins. The computations presented provide an interesting experimental component to the standard treatment of quantum spin in an undergraduate quantum mechanics course. |
Quantum information science and technology high school outreach: Conceptual progression for introducing principles and programming skills
| Pengarang | : | Dominik Schneble; Tzu-Chieh Wei; Angela M. Kelly |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 1) |
| Halaman | : | 88-97 |
| Abstrak | : | National data have shown the need to expand and diversify the talent pool of the quantum technologies workforce. This article describes a newly designed 25-h summer quantum information science and technology (QIST) program for high school students in grades 10–12; the goal is to advance physical science literacy and diversify the STEM pipeline through novel quantum science and quantum computing access and learning. This partnership between Stony Brook University and the New York Hall of Science was designed by quantum physicists and physics education researchers. This manuscript describes the rationale and progression of quantum ideas and computing skills introduced in the outreach program. The program design scaffolded physics, mathematics, and computer science concepts to engage high school students in the excitement of quantum information science and technology fields. The disciplinary content included the limitations of classical computing, classical and quantum physics principles (diffraction, polarization, wave-particle duality), the Mach–Zehnder interferometer, superposition, quantum thought experiments (Schrödinger's cat and Wigner's friend), entanglement and Bell's inequality, quantum key distribution, and basic quantum computing skills. Students also spent time visiting laboratories and museum exhibits and learning about academic progressions and career pathways in quantum technologies. This university-based science outreach model may be replicated by other quantum educators and adapted for learning in formal contexts. |