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We present the development and validation of a construct map addressing introductory quantum mechanics topics at the high school level, as a subset of a larger learning progression on quantum mechanics. Topics include energy quantization, photon absorption and emission, the Heisenberg uncertainty principle, atom stability, orbitals, wave function, and electronic properties of materials. To validate the hypothesized construct map, we designed a multiple-choice questionnaire and a 14-h teaching-learning sequence (TLS) designed in strict relation with the levels of the construct map. Twenty-three classes of Italian students (ages 17–18, N=408) were involved in the study: about half (N=200) were exposed to the TLS, while N=208 students received a typical textbook instruction on the same topics targeted by the construct map. Data were analyzed using a 1D Rasch model. Results show that the proposed construct map consistently describes the increasing abilities of students when exposed to instruction. In particular, when exposed to the TLS activities, students more likely move towards the upper levels of the construct map. Findings have implications for instruction designed to support students’ learning in quantum mechanics at the high school level.

Students’ ability to assess their own knowledge is an important skill in science education. However, students often overestimate their actual performances. In such cases, overconfidence bias arises. Previous studies in physics education have shown that overconfidence bias concerns mainly content areas, such as Newtonian mechanics, where misconceptions are strongly held by students. However, how the received instruction and the levels of understanding of a given topic influence overconfidence bias is yet to be proved. In this paper, we address this issue choosing as content area introductory quantum mechanics (QM). Overall, 408 high school students were involved in the study and randomly assigned to two experimental groups. One group received a textbook-based instruction about introductory QM, whereas the other one received instruction on the same topics through an innovative guided inquiry teaching-learning sequence (TLS), which included also potential pedagogical countermeasures for overconfidence bias. Students of both experimental groups completed a multiple-choice questionnaire and indicated for each item the degree of their confidence in the given answer using a 5-point Likert scale. The overconfidence bias was quantitatively defined and evaluated at person level using a 1D Rasch model. Progress in knowledge about the targeted topics was modeled according to a construct map validated in a previous paper. Results show that, for the whole sample, the overconfidence bias decreased as students progressed along the levels of the construct map. However, findings indicate that students of the TLS group achieved a significantly higher accuracy and a better confidence calibration, while the textbook group exhibited a lower performance and a significantly greater overconfidence bias. Implications for research into overconfidence bias in physics education are briefly discussed.

We present the design, statistical analysis, and validation of a questionnaire to assess students’ knowledge about basic aspects of quantum mechanics (QM). The QM evaluation (QME) is a true-false and multiple-choice mixed questionnaire that features 10 two-tier items spanning three relevant themes in quantum mechanics: wave behavior of matter, measurement, and atoms and electrons behavior. Its validity was assessed through a pilot administration to students and interviews with course instructors. We checked its internal consistency using both classic test theory and Rasch analysis to account for the different difficulty of each tier and for different scoring methods of the items. The questionnaire was administered to about 450 undergraduate physics students and high school physics teachers. Data show that it is a reliable instrument and all items have a good discriminatory power. Since the test does not require an advanced mathematical knowledge, it ideally lends itself to probe students’ knowledge about quantum mechanics in a variety of university courses, from the introductory ones to those more formal and mathematically oriented.

We report an empirical study on the development and validation of a learning progression (LP) in quantum mechanics (QM) at university level. Drawing on research results about students’ reasoning in QM, we designed a hypothetical LP (HLP) consisting of three Big Ideas: Measurement, A toms and Electrons, Wave function. We then developed ten Ordered-Multiple-Choice (OMC) items to assess the construct validity and hierarchy of HLP levels. We administered the questionnaire to 244 students attending the Bachelor in Physics, divided into three groups under different instruction conditions: no course, introductory course, introductory and upper-level course. An additional group of 43 non-physics students, who attended an introductory QM course, was also involved to inspect the role of physics background knowledge . We used exploratory factor analysis and Rasch analysis to analyse collected data. The results provided evidence for the revision of the HLP around only two Big Ideas – Atomic description and measurement; Wave function and its properties in the measurement process – which roughly match the topics covered in the introductory and upper-level courses, respectively. However, the hierarchy of hypothesised levels was substantially confirmed. Implications of our findings for the teaching of QM, and the improvement of the revised LP are also discussed.

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets |xn〉 defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed-form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.

International audience; We employed ab initio global structural prediction algorithms to obtain the ground-state structure of CuBO2 This is a very promising p-type transparent conductive oxide that was synthesized recently, and thought to belong to the delafossite family. We proved that the true ground state is certainly not the delafossite structure, and that the most promising candidate is a low symmetry monoclinic phase. This is still a layered structure, but with boron and copper having a different coordination with respect to the delafossite phase.

We present a description of the optical properties of a water-soluble BODIPY derivative in the gas phase and in water. Comparison with a hydrophobic BODIPY derivative with very similar structure but deprived of the hydrophilic groups, clarifies the effects of functionalization. The changes in solution are studied at different levels of modeling. In particular, we make use of Car–Parrinello molecular dynamics to take thermal motion into account, by generating a set of molecular configurations at about room temperature and embedding them in the polarizable continuum model (PCM) for the solvent. The theoretical scheme is that of time-dependent density functional theory which we apply using different approximations for the exchange-correlation functionals. Changes in the low-lying excitation spectrum (≈2.5–4.5 eV) of the solvated molecule in water relative to gas phase are shown to be due not only to the electrostatic interaction with the solvent but also to the thermal motion that induces a downward energy shift and broadening of the absorption lines. Addition of explicit water molecules to the PCM only affects spectral features at higher energies.

Oxygen vacancies at the SnO2(110) and (101) surface and subsurface sites have been studied in the framework of density functional theory by using both all-electron Gaussian and pseudopotential plane-wave methods. The all-electron calculations have been performed using the B3LYP exchange-correlation functional with accurate estimations of energy gaps and density of states. We show that bulk oxygen vacancies are responsible for the appearance of a fully occupied flat energy level lying at about 1 eV above the top valence band, and an empty level resonant with the conduction band. Surface oxygen vacancies strongly modify the surface band structures with the appearance of intragap states covering most of the forbidden energy window, or only a small part of it, depending on the vacancy depth from the surface. Oxygen vacancies can account for electron affinity variations with respect to the stoichiometric surfaces as well. A significant support to the present results is found by comparing them to the available experimental data.