group Small Group Activity

30 min.

Right Angles on Spacetime Diagrams
Theoretical Mechanics Fall 2020 Theoretical Mechanics Fall 2021

Special Relativity

Students take the inner product of vectors that lie on the spacetime axis to show that they are orthogonal. To do the inner product, students much use the Minkowski metric.

group Small Group Activity

60 min.

Expectation Value and Uncertainty for the Difference of Dice
Quantum Fundamentals Winter 2021

group Small Group Activity

60 min.

Going from Spin States to Wavefunctions

Wavefunctions quantum states probability amplitude histograms matrix notation of quantum states Arms representation

Arms Sequence for Complex Numbers and Quantum States

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.

group Small Group Activity

30 min.

Outer Product of a Vector on Itself

Projection Operators Outer Products Matrices

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).