From discrete states to wavefunctions

In the spin-first approach to learning quantum mechanics, students explore the 2-state spin Hilbert space before proceeding to wavefunctions and the related infinite-dimensional state space. In this note, we suggest a strategy to help students make this conceptual leap. Approximating continuous space with a finite number of locations, we construct a setting where students' intuition from spin space carries over to a position basis. We derive the position basis representations of the momentum and kinetic energy operators, solve simple bound state problems, and consider limitations to the discrete representation of position.