Questioning with university students on stationarity, time evolution and connection between sets of eigenstates in quantum mechanics

Conceptual change from a classical to a quantum perspective is a challenging task for students. Basic concepts such as state and time evolution, already posing problematic issues in classical physics, require a different interpretation because of the redefinition of the concept of state, inextricably linked to fundamental features of new system behavior such as incompatibility between observables. Within an empirical research aimed at investigating connections between conceptual aspects and formalism emerging from student reasoning, we designed questionnaire items to explore how student describe time evolution of states, how they identify stationary states and how they use related concepts of eigenstate of an observable and incompatibility between observables in this process. Data gathering instruments were developed through a case study to collect student points of view on the relevant issue. For each aspect, at least two items were designed in order to cross-examine from different perspectives. Data analysis was organized following qualitative research methodology. The questionnaire was administered to a small group of students together with follow-up interviews. The study shows that most students link energy eigenstates to stationary states, but inverse implication doesn’t emerge with the same strength. The relation between energy eigenstates and those of different observables is clearly stated only when a commutator expression is identified by students. Energy eigenstates and their linear combinations are related to time invariance and time evolution in quantum mechanics in familiar-abstract context of infinite well, while uncertainties emerge in the crucial situation of scattering. Students answer as expected to questions concerning familiar tasks and contexts, but this doesn’t correspond to conceptual understanding of crucial elements under investigation. There is a need to build competence on critical reasoning.