313 research outputs found
Unified connected theory of few-body reaction mechanisms in N-body scattering theory
A unified treatment of different reaction mechanisms in nonrelativistic N-body scattering is presented. The theory is based on connected kernel integral equations that are expected to become compact for reasonable constraints on the potentials. The operators T/sub +-//sup ab/(A) are approximate transition operators that describe the scattering proceeding through an arbitrary reaction mechanism A. These operators are uniquely determined by a connected kernel equation and satisfy an optical theorem consistent with the choice of reaction mechanism. Connected kernel equations relating T/sub +-//sup ab/(A) to the full T/sub +-//sup ab/ allow correction of the approximate solutions for any ignored process to any order. This theory gives a unified treatment of all few-body reaction mechanisms with the same dynamic simplicity of a model calculation, but can include complicated reaction mechanisms involving overlapping configurations where it is difficult to formulate models
Dominant partition method
By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails
Reinventing College Physics for Biologists: Explicating an epistemological curriculum
The University of Maryland Physics Education Research Group (UMd-PERG)
carried out a five-year research project to rethink, observe, and reform
introductory algebra-based (college) physics. This class is one of the Maryland
Physics Department's large service courses, serving primarily life-science
majors. After consultation with biologists, we re-focused the class on helping
the students learn to think scientifically -- to build coherence, think in
terms of mechanism, and to follow the implications of assumptions. We designed
the course to tap into students' productive conceptual and epistemological
resources, based on a theoretical framework from research on learning. The
reformed class retains its traditional structure in terms of time and
instructional personnel, but we modified existing best-practices curricular
materials, including Peer Instruction, Interactive Lecture Demonstrations, and
Tutorials. We provided class-controlled spaces for student collaboration, which
allowed us to observe and record students learning directly. We also scanned
all written homework and examinations, and we administered pre-post conceptual
and epistemological surveys. The reformed class enhanced the strong gains on
pre-post conceptual tests produced by the best-practices materials while
obtaining unprecedented pre-post gains on epistemological surveys instead of
the traditional losses.Comment: 35 pages including a 15 page appendix of supplementary material
Symbolic Manipulators Affect Mathematical Mindsets
Symbolic calculators like Mathematica are becoming more commonplace among
upper level physics students. The presence of such a powerful calculator can
couple strongly to the type of mathematical reasoning students employ. It does
not merely offer a convenient way to perform the computations students would
have otherwise wanted to do by hand. This paper presents examples from the work
of upper level physics majors where Mathematica plays an active role in
focusing and sustaining their thought around calculation. These students still
engage in powerful mathematical reasoning while they calculate but struggle
because of the narrowed breadth of their thinking. Their reasoning is drawn
into local attractors where they look to calculation schemes to resolve
questions instead of, for example, mapping the mathematics to the physical
system at hand. We model the influence of Mathematica as an integral part of
the constant feedback that occurs in how students frame, and hence focus, their
work
Epistemic Complexity and the Journeyman-Expert Transition
Physics students can encounter difficulties in physics problem solving as a
result of failing to use knowledge that they have but do not perceive as
relevant or appropriate. In previous work the authors have demonstrated that
some of these difficulties may be epistemological. Students may limit the kinds
of knowledge that they use. For example, they may use formal manipulations and
ignore physical sense making or vice versa. Both beginning (novice) and
intermediate (journeymen) students demonstrate these difficulties. Learning
both to switch one's epistemological lens on a problem and to integrate
different kinds of knowledge is a critical component of learning to solve
problems in physics effectively. In this paper, we present two case studies in
which journeyman students (upper-division physics majors) demonstrate switching
between epistemological resources in approaching a complex problem. We
conjecture that mastering these epistemological skills is an essential
component of learning complex problem solving in physics.Comment: 12 page
Addressing student models of energy loss in quantum tunnelling
We report on a multi-year, multi-institution study to investigate student
reasoning about energy in the context of quantum tunnelling. We use ungraded
surveys, graded examination questions, individual clinical interviews, and
multiple-choice exams to build a picture of the types of responses that
students typically give. We find that two descriptions of tunnelling through a
square barrier are particularly common. Students often state that tunnelling
particles lose energy while tunnelling. When sketching wave functions, students
also show a shift in the axis of oscillation, as if the height of the axis of
oscillation indicated the energy of the particle. We find inconsistencies
between students' conceptual, mathematical, and graphical models of quantum
tunnelling. As part of a curriculum in quantum physics, we have developed
instructional materials to help students develop a more robust and less
inconsistent picture of tunnelling, and present data suggesting that we have
succeeded in doing so.Comment: Originally submitted to the European Journal of Physics on 2005 Feb
10. Pages: 14. References: 11. Figures: 9. Tables: 1. Resubmitted May 18 with
revisions that include an appendix with the curriculum materials discussed in
the paper (4 page small group UW-style tutorial
Learning physics in context: a study of student learning about electricity and magnetism
This paper re-centres the discussion of student learning in physics to focus
on context. In order to do so, a theoretically-motivated understanding of
context is developed. Given a well-defined notion of context, data from a novel
university class in electricity and magnetism are analyzed to demonstrate the
central and inextricable role of context in student learning. This work sits
within a broader effort to create and analyze environments which support
student learning in the sciencesComment: 36 pages, 4 Figure
Making Sense of the Legendre Transform
The Legendre transform is an important tool in theoretical physics, playing a
critical role in classical mechanics, statistical mechanics, and
thermodynamics. Yet, in typical undergraduate or graduate courses, the power of
motivation and elegance of the method are often missing, unlike the treatments
frequently enjoyed by Fourier transforms. We review and modify the presentation
of Legendre transforms in a way that explicates the formal mathematics,
resulting in manifestly symmetric equations, thereby clarifying the structure
of the transform algebraically and geometrically. Then we bring in the physics
to motivate the transform as a way of choosing independent variables that are
more easily controlled. We demonstrate how the Legendre transform arises
naturally from statistical mechanics and show how the use of dimensionless
thermodynamic potentials leads to more natural and symmetric relations.Comment: 11 pages, 3 figure
Analyzing Problem Solving Using Math in Physics: Epistemological Framing via Warrants
Developing expertise in physics entails learning to use mathematics
effectively and efficiently as applied to the context of physical situations.
Doing so involves coordinating a variety of concepts and skills including
mathematical processing, computation, blending ancillary information with the
math, and reading out physical implications from the math and vice versa. From
videotaped observations of intermediate level students solving problems in
groups, we note that students often "get stuck" using a limited group of skills
or reasoning and fail to notice that a different set of tools (which they
possess and know how to use effectively) could quickly and easily solve their
problem. We refer to a student's perception/judgment of the kind of knowledge
that is appropriate to bring to bear in a particular situation as
epistemological framing. Although epistemological framing is often unstated
(and even unconscious), in group problem solving situations students sometimes
get into disagreements about how to progress. During these disagreements, they
bring forth explicit reasons or warrants in support of their point of view. For
the context of mathematics use in physics problem solving, we present a system
for classifying physics students' warrants. This warrant analysis offers
tangible evidence of their epistemological framing.Comment: 23 page
On the Importance of Engaging Students in Crafting Definitions
In this paper we describe an activity for engaging students in crafting definitions. We explore the strengths of this particular activity as well as the broader implications of engaging students in crafting definitions more generally
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