相关论文: Student reasoning about measurement uncertainty in…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
Covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity -- has been examined extensively in mathematics education research. Little research has been done, however, on covariational…
Most introductory quantum physics instructors would agree that transitioning students from classical to quantum thinking is an important learning goal, but may disagree on whether or how this can be accomplished. Although (and perhaps…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Effective physics learning, especially in complex topics, requires balancing mathematical formalism with conceptual understanding. Conceptual problem-solving involves connecting math to physical reality, and using an epistemological…
Measurement in quantum mechanics is notoriously unpredictable. The uncertainty in quantum measurement can arise from the noncommutativity between the state and the measurement basis which is intrinsically quantum, but it may also be of…
We have been investigating the difficulties that students in upper-level undergraduate courses have in determining the probability distribution for measuring energy and position as a function of time when the initial wave function is…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
In an educational setting, an estimate of the difficulty of multiple-choice questions (MCQs), a commonly used strategy to assess learning progress, constitutes very useful information for both teachers and students. Since human assessment…
Large language models (LLMs) have demonstrated remarkable capabilities in solving complex reasoning tasks, particularly in mathematics. However, the domain of physics reasoning presents unique challenges that have received significantly…
Covariational reasoning--considering how changes in one quantity affect another, related quantity--is a foundation of quantitative modeling in physics. Understanding quantitative models is a learning objective of introductory physics…
We compare the proposals that have appeared in the literature to describe a measurement of the time of arrival of a quantum particle at a detector. We show that there are multiple regimes where different proposals give inequivalent,…
Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied…
We investigate student comfort with the material in an upper-division spins-first quantum mechanics course. Pre-lecture surveys probing students' comfort were administered weekly, in which students assigned themselves a "discomfort level"…
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
As part of ongoing investigations into student learning in advanced undergraduate courses, we have developed a conceptual assessment tool for upper-division electrodynamics (E&M II): the Colorado UppeR-division ElectrodyNamics Test…
Science students must deal with the errors inherent to all physical measurements and be conscious of the necessity to express their as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic.…