The instructor and students do a skit where students represent quantum states that are “measured” by the instructor resulting in a state collapse.
The instructor ask for volunteers for an activity that is a conceptual play of what happens during a quantum measurement.
The instructor can remind students of the prerequisite understandings as a lead into the activity.
The instructor selects the projection operator corresponding to the result and lets that operator act on the state.
\[\Big(|+\rangle_y \;_y\langle+|\Big)|\psi_{student}\rangle\]
The student renormalizes their state.
\[|\psi_{new}\rangle = \cancel{_y\langle+|\psi_{student}\rangle}|+\rangle_y\]
accessibility_new Kinesthetic
30 min.
distance formula coordinate systems dot product vector addition
A short improvisational role-playing skit based on the Star Trek series in which students explore the definition and notation for position vectors, the importance of choosing an origin, and the geometric nature of the distance formula. \[\vert\vec{r}-\vec{r}^\prime\vert=\sqrt{(x-x^\prime)^2+(y-y^\prime)^2-(z-z^\prime)^2}\]accessibility_new Kinesthetic
10 min.
group Small Group Activity
30 min.
group Small Group Activity
60 min.
Each small group of 3-4 students is given a white board or piece of paper with a square grid of points on it.
Each group is given a different two-dimensional vector \(\vec{k}\) and is asked to calculate the value of \(\vec{k} \cdot \vec {r}\) for each point on the grid and to draw the set of points with constant value of \(\vec{k} \cdot \vec{r}\) using rainbow colors to indicate increasing value.
accessibility_new Kinesthetic
10 min.
density charge density mass density linear density uniform idealization
Students, pretending they are point charges, move around the room acting out various prompts from the instructor regarding charge densities, including linear \(\lambda\), surface \(\sigma\), and volume \(\rho\) charge densities, both uniform and non-uniform. The instructor demonstrates what it means to measure these quantities. In a remote setting, we have students manipulate 10 coins to model the prompts in this activity and the we demonstrate the answers with coins under a doc cam.group Small Group Activity
10 min.
computer Mathematica Activity
30 min.
group Small Group Activity
5 min.
group Small Group Activity
60 min.
Wavefunctions quantum states probability amplitude histograms matrix notation of quantum states Arms representation
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
5 min.