This activity lets students explore translating a wavefunction that isn't obviously made up of eigenstates at first glance into ket and matrix form. Then students explore wave functions, probabilities in a region, expectation values, and what wavefunctions can tell you about measurements of \(L_z\).

Students review using the Arms representation to represent states for discrete quantum systems and connecting the Arms representation to histogram and matrix representation. The student then extend the Arms representation to begin exploring the continuous position basis.