Investigating and improving student understanding of time dependence of expectation values in quantum mechanics using an interactive tutorial on Larmor precession

We studied the challenges students face with time dependence in quantum mechanics, specifically in the context of Larmor precession of spin. This research informed the creation and evaluation of a learning tutorial aimed at helping students grasp these concepts using a two-state system. The tutorial utilizes visualization tools to enhance students' intuition and emphasizes the integration of qualitative and quantitative understanding. We also examine how students applied semi-classical or quantum mechanical reasoning in their answers and assess the improvement they showed after working with the tutorial.