Activities
Students compute the outer product of a vector on itself to product a projection operator. Students discover that projection operators are idempotent (square to themselves) and that a complete set of outer products of an orthonormal basis is the identity (a completeness relation).
Whole Class Activity
10 min.
A group of students, tethered together, are floating freely in outer space. Their task is to devise a method to reach a food cache some distance from their group.
Students perform an inner product between two spin states with the arms representation.
Students compute inner products to expand a wave function in a sinusoidal basis set. This activity introduces the inner product for wave functions, and the idea of approximating a wave function using a finite set of basis functions.