Characterizations of student, instructor, and textbook discourse related to basis and change of basis in quantum mechanics

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community's social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic, socially acquired language in two classroom communities that we consider to be subcultures of the broader community of physicists. We perform a discourse analysis on twelve quantum mechanics students, two instructors, and the course text related to statements about basis and change of basis within a spin-1/2 probability problem. We classify the utterances' grammatical constructions and situated meanings. Results show that students and instructors' utterances referred to a person, calculation, vector being in, or vector written in a basis. Utterances in these categories had similar situated meanings and were used similarly by the students and instructors. Utterances referred to change of basis as changing the form of a vector, writing the vector in another way, changing the vector into another vector, or switching bases. Utterances in these categories had varying situated meanings and were used similarly by the students and instructors. The students and instructors often switched between different discourse types in quick succession. We found similar utterance types, situated meanings, and grammatical constructions across students and instructors. The textbook's discourse sometimes differed from the discourse of the students and instructors. Within this study, the students and instructors were from two universities, yet they spoke similar utterances when referring to basis and change of basis. This gives evidence to their shared social language with a broader community of physicists. Integrating and leveraging social languages in the classroom could facilitate students' enculturation into the classroom and broader professional community.