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A free Gaussian can be thought of as the ground state of a simple harmonic oscillator with the frequency adjusted to give the initial variance of the Gaussian. The free Hamiltonian, when expressed in terms of the raising and lowering operators, can be thought of as a squeezing operator acting on the SHO ground state. We show how this mapping can be used to understand the increasing variance of the Gaussian as it evolves in time. In cases where time evolution is taught after the operator method solution of the SHO, then one can explain free expansion in this alternative framework. One can even perform the calculation using only operator manipulations, instead of solving the time-dependent Schroedinger equation. We sketch how this is done. It requires the Weyl form of the BCH formula, the Hadamard lemma, and the exponential disentangling identity. This work was an REU project.

AAPT WM 22

Free expansion of a Gaussian via squeezed harmonic oscillator states

squeezed states

free-expansion gaussian wavepacket

representation-independent

operator-first

quantum mechanics

Join AAPT and Physics Educators worldwide in developing and strengthening your professional connections by attending the 2021 AAPT Virtual Summer Meeting. AAPT meetings are a great way to reflect on your teaching, recommit to best practices and re-energize your career with new research, products, and techniques.

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This meeting is a great opportunity to explore sessions and workshops designed with your professional development in mind. Present your research and exchange ideas on the latest in teaching and pedagogy. Participate in a wide range of events, activities, plenaries, and so much more, connecting you with peers and colleagues who share your commitment to excellence in physics education.

One of the broad concerns about the future of physics education research is a relative paucity of active PER groups at colleges and universities that are not primarily focused upon research. Yet, institutions that are primarily focused on teaching need to replicate these studies directly, whether to confirm that results at different university types are similar, or to identify differing outcomes that are connected to institutional type. Differences in institutional focus attract different student populations, and hence, different student motivations, which can directly affect data results from long-recognized quantitative and qualitative measuring instruments. This poster outlines a preliminary “lay of the land” view from the perspective of a solo PER researcher working at a regional comprehensive state university – both as an example of a non-research university and looking at other teaching-focused institution types – in order to determine the current outlook of PER’s growth outside the research university.

PER outside Research Universities: A Solo PER Perspective

Amazon Prime's much-anticipated television adaptation of The Wheel of Time book series premiered in November 2021. The series is based on broadly acclaimed source material and features a talented and diverse cast and writing staff. With a market continuing to demand high-fantasy entertainment, the show is expected to entertain for years to come. This premiere also presents an opportunity for physics educators to engage with students, as the original series author, the late Robert Jordan, majored in physics and consistently incorporated his physics background into the story’s setting. I review some of the history of this series and outline thoughts for how we might use this material to engage our students in discussion of physics concepts and representation in the physics community.

Engaging Physics Students with The Wheel of Time

The standard view is that space and time act together, putting&nbsp;aside the energetic component, leaving STR to paradox over it. GTR clears this up and deals, inclusively, with accelerated frames, where energy acting over spacetime is the essential part of the GTR equation. Still, the primary attention is over, the challenged to imagine Minkowski's 4-dimensional spacetime. Their representation commonly expresses a curved space & time consequence of energy over spacetime instead from its origins, the equivalent moving space by the presence of proper energy and the surrounding ones.

An Intuitive Way to Understand Curved Spacetime

This talk describes a two-week module on astrodynamics developed for incoming STEM students. The goal of the module is for students to design and simulate a mission from Earth to Venus using the Hohmann transfer---a space maneuver used to travel between two planetary orbits. This application was selected because it utilizes a variety of introductory physics topics. The participants were all low-income, Pell-eligible college students; most were Black, Hispanic, and/or first-generation college students. This group is most at risk of leaving STEM, yet 80% of students who took this course were retained in STEM. In this talk we will present the course learning objectives, details of the Hohmann transfer simulation in VPython, and student outcomes including grades, retention rates, and survey results. This module could be replicated at the high school or college levels to help students achieve proficiency in programming while learning basic physics and astronomy content.

Summer Short Course on Astrodynamics for Incoming STEM Majors

Physics remains an area of STEM with lower amounts of diversity among the student population, therefore it becomes important to consider how classroom culture may contribute to a lack of belonging for students in underrepresented groups. This study aimed to determine how students in physics courses at Miami University perceived peer interactions in their courses during formal and informal group work. Virtual interviews were conducted with nine physics majors and responses were coded for positive and negative statements related to themes of respect, contribution, outcome of the task and overall class culture. It was found that on average male students had a higher percentage of positive statements about class culture, while female students had a higher percentage of positive statements about task outcomes and a higher percentage of negative statements about communication and class culture.

Perceived Effectiveness of Peer Interaction in Physics Courses

Most people likely think of learning the constellations of the night sky when they think of planetariums, but that’s not going to help you teach physics; It may not even really be astronomy, but more like sky geography; I think it’s important to teach astronomy and physics whenever possible, and planetariums can help with so much more than just constellations; Planetariums can do things that regular classrooms cannot do. This in-dome presentation will look at both specific and general ways that planetariums can help you teach physics and astronomy.

Planetarium Potentials

The STEP UP project (STEPUPphysics.org) was designed to reduce barriers for high school women in physics and encourage them to pursue an undergraduate physics degree, in which women have been underrepresented historically. STEP UP focuses on implementing high school interventions by recruiting high school physics teachers, called Advocates, who are trained to teach STEP UP’s research-driven materials in their classroom. To understand the effects of material implementation on Advocates, surveys are being administered to them before and after the school year. Using a “tempered radicals” framing, this talk will present an analysis of initial survey responses describing the characteristics of teachers who are willing to be disruptive in order to reduce barriers for women and change the physics classroom culture. Results will inform our understanding of teachers and the ways in which we can support their development as tempered radicals.

Identifying Tempered Radicals in the STEP UP Advocate Program

The 2021 Inclusive Curriculum in Physics Workshop Series is a three part series organized and led by the National Society of Black Physicists, the National Society of Hispanic Physicists, and the American Association of Physics Teachers. The series leverages the expertise of equity, diversity and inclusion (EDI) experts, as well as an organizing team of physics students, faculty and STEM professionals at different stages of their studies and careers.The purpose of the series is to: Explore the importance of EDI in the classroom and the existing instructional materials that focus on EDI, with members of the broad physics education community; Engage participants in discussion and action items around the current challenges to equity in STEM education with input from experts in the field; Provide support to working groups through a network of partners to engage in specific physics education projects using the lens of inclusion.

The 2021 Inclusive Curriculum in Physics Workshop Series

In Advanced Lab classes, students often perform labs on radioactivity and nuclear spectroscopy as well as labs measuring several fundamental constants. Advanced labs classes can pose a problem for smaller public institutions as these classes usually have low enrollments and having multiple traditional lab setups is costly. However, advances in digital electronics have enabled the development of low cost ($2000), easy to use nuclear spectroscopy systems that can provide multiple lab activities. In addition to the traditional radioactivity and shielding labs, these systems can also be used with exempt radioactive sources to provide other laboratory activities including measuring to around 5%: 1) the charge of an electron using x-ray fluorescence and 2) the mass of an electron using Compton scattering. This eliminates the need for additional laboratory equipment making such labs more accessible to both undergraduate institutions and high schools.

A Simple Nuclear Lab To Measure The Electron's Rest Mass

It is customary to introduce students to quantum mechanics with the Schrödinger equation because the single-component wave function is easy to handle mathematically. However, the Schrödinger equation is not consistent with special relativity, nor does it describe spin angular momentum. We propose that the Dirac equation provides a better introduction because (1) it is consistent with the laws of physics, (2) it describes spin angular momentum, and (3) it is easily derived from the classical physics model of an ideal elastic solid. The resultant description of classical wave mechanics shares many features of relativistic quantum mechanics. These include Lorentz invariance, bispinor wave functions, half-integer azimuthal quantum numbers, standing waves with circular wave propagation, particle classifications similar to fermions and bosons, operators for physical quantities including spin angular momentum, Pauli exclusion principle, and interaction via potentials. The Schrödinger equation approximates the evolution of a single wave function component.

Free expansion of a Gaussian via squeezed harmonic oscillator states

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Free expansion of a Gaussian via squeezed harmonic oscillator states

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PER outside Research Universities: A Solo PER Perspective

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