Student understandings of discrete and continuous in quantum mechanics: A thematic analysis

Students in a spins-first quantum mechanics course often have difficulties transitioning from spin systems to continuous systems like the infinite square well. Our study investigates how students understand discrete and continuous quantities in quantum mechanics and the connections the students make between them. We interviewed six students who were concurrently enrolled in a junior-level spins-first quantum mechanics course with a computational lab. During the interview, students organized a set of 20 cards containing various quantum mechanics concepts and representations, including snippets of ython code. Using a phenomenographic approach, we generated four themes: understandings of discrete, understandings of continuous, discreteness of representations, and discrete approximations of integrals. Participants often related discrete and continuous quantities in the context of code, suggesting that computational activities can support students in transitioning from discrete systems to continuous ones.