title, topic, keyword
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Required in-class time for activities
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Small Group Activity

30 min.

Outer Product of a Vector on Itself
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).
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.
  • Found in: Central Forces course(s)


30 min.

Inner Products with Arms
Students perform an inner product between two spin states with the arms representation.

Computational Activity

120 min.

Sinusoidal basis set
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.