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Abstract Knowledge of quantum mechanical systems is becoming more important for many science and engineering students who are looking to join the emerging quantum workforce. To better prepare a wide range of students for these careers, we must seek to develop new tools to enhance our education in quantum topics. We present initial studies on the use of one of these such tools, Quantum Composer, a 1D quantum simulation and visualization tool developed for education and research purposes. In particular, we conducted five think-aloud interviews with students who worked through an exercise using Quantum Composer that focused on the statics and dynamics of quantum states in a single harmonic well system. Our results show that Quantum Composer helps students to obtain the correct answers to the questions posed, but additional support is needed to facilitate the development of student reasoning behind these answers. We also show that students are able to focus only on the relevant features of Quantum Composer to achieve the task. 

Abstract The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier–Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical, i.e., there is a ‘scaling gap’ between what can be established by mathematical analysis and what is needed to rule out a singularity. A recently introduced mathematical framework—based on a suitably defined ‘scale of sparseness’ of the regions of intense vorticity—brought the first scaling reduction of the NS super-criticality since the 1960s. Here, we put this framework to the first numerical test using a spatially highly resolved computational simulation performed near a ‘burst’ of the vorticity magnitude. The results confirm that the scale is well suited to detect the onset of dissipation and provide numerical evidence that ongoing mathematical efforts may succeed in closing the scaling gap. 

As education researchers gain a broader understanding of how students learn quantum mechanics, new pedagogical and technical resources are being developed to facilitate student learning. To further research-based knowledge of student learning of quantum mechanics, we present a study on the use of Quantum Composer, a flexible, flow-based tool for the exploration and simulation of quantum mechanical systems in one dimension. To explore Composer’s impact on students’ knowledge of quantum mechanics, we carried out think-aloud interviews where students worked through an exercise exploring the statics and time-dynamics of quantum states in single and double harmonic well potentials. Student Outcomes are then cross-coded with their observed Interactions with Composer. We find that defined Outcomes of Recollection, Reinforcement and Discovery happen most often when students are using the Composer tools that allow them to visualize quantum states, simulate their time dynamics, and change parameters repeatedly in order to understand how systems are represented in both the static and dynamic cases.