This paper draws on part of a larger project looking at university students' learning difficulties associated with quantum mechanics. Here an unexpected and interesting aspect was brought to the fore while students were discussing a computer simulation of one-dimensional quantum scattering and tunnelling. In these explanations the most dominant conceptual hurdle that emerged in the students' explanations was centred around the notion of probability. To explore this further, categories of description of the variation in the understanding of probability were constituted. The analysis reported is done in terms of the various facets of probability encountered in the simulation and characterizes dynamics of this conceptual hurdle to appropriate understanding of the scattering and tunnelling process. Pedagogical implications are discussed.
Students’ attitudes and beliefs about learning have been shown to affect learning outcomes. This study explores how university physics students think about what it means to understand physics equations. The data comes from semi-structured interviews with students from three Swedish universities. The analysis follows a data-based, inductive approach to characterise students’ descriptions of what it means to understand equations in terms of epistemological mindsets (perceived critical attributes of a learning, application, or problem-solving situation that are grounded in epistemology). The results are given in terms of different components of students’ epistemological mindsets. Relations between individuals and sets of components as well as differences across various stages of students’ academic career are then explored. Pedagogical implications of the findings are discussed and tentative suggestions for university physics teaching are made.
In this paper we consider a scenario, consisting of a de Sitter phase followed by a phase described by a scale factor a(t) ∼ t q , where 1/3 < q < 1, which can be viewed as an inflationary toy model. It is argued that this scenario naively could lead to an information paradox. We propose that the phenomenon of Poincaré recurrences plays a crucial role in the resolution of the paradox. We also comment on the relevance of these results to inflation and the CMBR.
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