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.

This is a thesis which contributes to research in two different fields: theoretical physics and physics education research. The common link between these two areas is that both involve explorations of abstract physics and mathematical representations, but from different perspectives.

This thesis is concerned with research in two very different fields, theoretical physics and physics education research. As a thesis in physics education these two research components are drawn together by what is becoming increasingly known as /the scholarship of teaching/ under a common focus that I have defined as abstract physics. The first part of this thesis clarifies how these two constructs are used to integrate the components of the thesis.