*group*A glass of water*group*Small Group Activity30 min.

##### A glass of water

Energy and Entropy 2021 (2 years)thermodynamics intensive extensive temperature volume energy entropy

Students generate a list of properties a glass of water might have. The class then discusses and categorizes those properties.*group*Applying the equipartition theorem*group*Small Group Activity30 min.

##### Applying the equipartition theorem

Contemporary Challenges 2021 (4 years) Students count the quadratic degrees of freedom of a few toy molecules to predict their internal energy at temperature \(T\).*groups*Pineapples and Pumpkins*groups*Whole Class Activity10 min.

##### Pineapples and Pumpkins

Static Fields 2023 (6 years)There are two versions of this activity:

As a whole class activity, the instructor cuts a pumpkin in order to produce a small volume element \(d\tau\), interspersing their work with a sequence of small whiteboard questions. This version of the activity is described here.

As a small group activity, students are given pineapple rounds and pumpkin wedges to explore area volume elements in cylindrical and spherical coordinate systems. In this version of the activity, the fruit is distribued to the students with appropriate children's pumpkin cutting equipment, as part of activities Vector Differential--Curvilinear, Scalar Surface and Volume Elements, or Vector Surface and Volume Elements.

*face*Equipartition theorem*face*Lecture30 min.

##### Equipartition theorem

Contemporary Challenges 2021 (4 years) This lecture introduces the equipartition theorem.*group*Gaussian Parameters*group*Small Group Activity10 min.

##### Gaussian Parameters

Periodic Systems 2022 Students use an applet to explore the role of the parameters \(N\), \(x_o\), and \(\sigma\) in the shape of a Gaussian \begin{equation} f(x)=Ne^{-\frac{(x-x_0)^2}{2\sigma^2}} \end{equation}*group*Fourier Transform of a Shifted Function*assignment*Spin Three Halves Time Dependence*assignment*Homework##### Spin Three Halves Time Dependence

Quantum Fundamentals 2023 A spin-3/2 particle initially is in the state \(|\psi(0)\rangle = |\frac{1}{2}\rangle\). This particle is placed in an external magnetic field so that the Hamiltonian is proportional to the \(\hat{S}_x\) operator, \(\hat{H} = \alpha \hat{S}_x \doteq \frac{\alpha\hbar}{2}\begin{pmatrix} 0 & \sqrt{3} & 0 & 0\\ \sqrt{3} & 0 & 2 & 0\\ 0 & 2 & 0 & \sqrt{3} \\ 0 & 0 & \sqrt{3} & 0 \end{pmatrix}\)- Find the energy eigenvalues and energy eigenstates for the system.
- Find \(|\psi(t)\rangle\).
- List the outcomes of all possible measurements of \(S_x\) and find their probabilities. Explicitly identify any probabilities that depend on time.
- List the outcomes of all possible measurements of \(S_z\) and find their probabilities. Explicitly identify any probabilities that depend on time.

*assignment_ind*Normalization of the Gaussian for Wavefunctions*assignment_ind*Small White Board Question5 min.

##### Normalization of the Gaussian for Wavefunctions

Periodic Systems 2022 Students find a wavefunction that corresponds to a Gaussian probability density.*assignment*Building the PDM: Instructions*assignment*Homework##### Building the PDM: Instructions

PDM Energy and Entropy 2021 (2 years) In your kits for the Portable Partial Derivative Machine should be the following:- A 1ft by 1ft board with 5 holes and measuring tapes (the measuring tapes will be on the
**top**side) - 2 S-hooks
- A spring with 3 strings attached
- 2 small cloth bags
- 4 large ball bearings
- 8 small ball bearings
- 2 vertical clamp pulleys
- A ziploc bag containing
- 5 screws
- 5 hex nuts
- 5 washers
- 5 wing nuts
- 2 horizontal pulleys

- one screw should be put through each hole so that the threads stick out through the top side of the board. Next use a hex nut to secure
**each**screw in place. It is not critical that they be screwed on any more than you can comfortably manage by hand. - After securing all 5 screws in place with a hex nut, put a washer on each screw.
- Slide a horizontal pulley onto screws 1 and 2 (as labeled above).
- On all 5 screws, add a wing nut to secure the other pieces. Again, it does not need to be tightened all the way as long as it is secure enough that nothing will fall off.
- Using the middle wingnut/washer/screw (Screw 4), clamp the shortest of the strings tied to the spring.
- Loop the remaining 2 looped-ends of string around the horizontal pulleys and along the measuring tape.
- Using the string as a guide, clamp the vertical pulleys into place on the edge of the board.
- Through the looped-end of each string, place 1 S-hook.
- Put the other end of each s-hook through the hole in the small cloth bag.

- A 1ft by 1ft board with 5 holes and measuring tapes (the measuring tapes will be on the
*group*Fourier Transform of the Delta Function*group*Small Group Activity5 min.

##### Fourier Transform of the Delta Function

Periodic Systems 2022 Students calculate the Fourier transform of the Dirac delta function.- Energy and Entropy 2021 (2 years) The spring constant \(k\) for a one-dimensional spring is defined by: \[F=k(x-x_0).\] Discuss briefly whether each of the variables in this equation is extensive or intensive.