Related papers: Student difficulties with quantum states while tra…

In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed…

We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research,…

Resonance plays critical roles in the formation of many physical phenomena, and many techniques have been developed for the exploration of resonance. In a recent letter [Phys. Rev. Lett. 117, 062502 (2016)], we proposed a new method for…

A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this…

Research-validated multiple-choice questions comprise an easy-to-implement instructional tool for scaffolding student learning and providing formative assessment of students' knowledge. We present findings from the implementation of a…

Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…

Resonance plays critical roles in the formation of many physical phenomena, and several methods have been developed for the exploration of resonance. In this work, we propose a new scheme for resonance by solving the Dirac equation in…

We describe the difficulties advanced undergraduate and graduate students have with quantum measurement. To reduce these difficulties, we have developed research-based learning tools such as the Quantum Interactive Learning Tutorial (QuILT)…

A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…

We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian…

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the degenerate perturbation theory. The investigation was carried out in…

We present a method enabling us to write in relativistic manner the wave function of some particular two particle bound state models in quantum mechanics. The idea is to expand the bound state wave function in terms of free states and to…

The Dirac delta function can be defined by the limitation of the rectangular function covering a unit area with decrease of the width of the rectangle to zero, and in quantum mechanics the eigenvectors of the position operator take the form…

Expanding our knowledge of student difficulties in advanced undergraduate electromagnetism is essential if we are to develop effective instructional interventions. Drawing on an analysis of course materials, in-class observations and…

By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory…

We discuss an investigation exploring students' difficulties with equations involving resistance, capacitance and inductance. We find that introductory physics students have great difficulty understanding, e.g., how the resistance of an…

This work aims to shed some light on the meaning of the positive energy assumption in relativistic quantum theory and its relation to questions of localization of quantum systems. It is shown that the positive energy property of solutions…

The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove…

Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…

In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…