From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics

Abstract

We conducted a multiyear project across three institutions to develop an instructional tutorial that supports student understanding of change of basis in quantum mechanics. Building from our previous work, we identified learning goals to guide activity development. The tutorial makes an analogy between spin-1/2 states and a Cartesian coordinate system. This paper details the iterative development process including reports of observations from classroom implementations and the resulting modifications to the activity. Further, we report preliminary findings on the success of the activity in improving students' ability to correctly change basis and their articulation that change of basis is a choice of representation, not a change to the physical system.