n order to support students in the development of expertise in quantum mechanics (QM), as well as to provide insight on teaching, we asked which concepts and structures can act as organizing principles in basic QM (RQ1). The research question has been addressed in a multi-step process based on the analysis of categorization studies, on a content analysis of a sample of upper-undergraduate course textbooks and on the results of existing research on learning difficulties in QM. The answer to RQ1 consists in seven concept maps, intended as models of the organizing principles of quantum knowledge needed to account for the results of measurement and time evolution both at a qualitative and quantitative level. The central element of this network is the interplay of the vector structure of the quantum states and the operator structure of the observables, with a particular focus on the relations between observables. These relations explain how information on measurement and time evolution is encoded in the modulus and in the phase of the probability amplitudes associated with the representations of the state, a topic identified as difficult by educational research. At upper-undergraduate level, the maps can be used by instructors as a support for helping students build a well-organized knowledge structure independently of the approach used, be it a spin-first or a waves-first one. However, this framework provides indications in favor of the former over the latter. At high school level, a simplified version of this framework has been used as a basis for the design of a teaching-learning sequence.
23 pages, 9 figures, 1 table
The Delicate Dance of Orbital Rendezvous: https://arxiv.org/abs/1908.02592
The meeting of two spacecraft in orbit around a planet or moon involves a delicate dance that must carefully the balance the gravitational, Coriolis, and centrifugal forces acting on the spacecraft. The intricacy of the relative motion between the two spacecraft caused problems for the Gemini missions in the mid-1960s. Although now mastered, the problem of how to bring two orbiting objects together continues to be misrepresented in popular movies and books. In this article, I will consider the case when the two spacecraft are in close proximity (compared with the radii of their orbits), and examine the counter-intuitive trajectories that are needed to bring them together. I will examine how a stranded astronaut might use an impulsive force to return to her ship in Earth orbit, how and when line-of-sight targeting may be used for a rendezvous, and how the Apollo 11 lunar module executed a Terminal Phase Initiation maneuver to rendezvous with the command/service module as they both circled the Moon.
29 pages, 15 figures. Published by the American Journal of Physics