assignment_ind Small White Board Question

30 min.

Magnetic Moment & Stern-Gerlach Experiments
Quantum Fundamentals 2022 (2 years)

Angular Momentum Spin Magnetic Moment Stern-Gerlach Experiments

Students consider the relation (1) between the angular momentum and magnetic moment for a current loop and (2) the force on a magnetic moment in an inhomogeneous magnetic field. Students make a (classical) prediction of the outcome of a Stern-Gerlach experiment.

group Small Group Activity

30 min.

Name the experiment (changing entropy)
Energy and Entropy 2021 (2 years)

thermodynamics entropy experiment derivative first law

Students are placed into small groups and asked to create an experimental setup they can use to measure the partial derivative they are given, in which entropy changes.

group Small Group Activity

30 min.

de Broglie wavelength after freefall
Contemporary Challenges 2022 (3 years)

de Broglie wavelength gravity

In this activity students combine energy conservation with the relationship between the de Broglie wavelength and momentum to find the wavelength of atoms that have been dropped a given distance.

group Small Group Activity

10 min.

Sequential Stern-Gerlach Experiments
Quantum Fundamentals 2022 (2 years)

group Small Group Activity

30 min.

Name the experiment
Energy and Entropy 2021 (3 years)

partial derivatives experiment thermodynamics

Student groups design an experiment that measures an assigned partial derivative. In a compare-and-contrast wrap-up, groups report on how they would measure their derivatives.

group Small Group Activity

30 min.

“Squishability” of Water Vapor (Contour Map)

Thermo Partial Derivatives

Students determine the “squishibility” (an extensive compressibility) by taking \(-\partial V/\partial P\) holding either temperature or entropy fixed.

group Small Group Activity

30 min.

Expectation Values for a Particle on a Ring
Central Forces 2022 (2 years)

central forces quantum mechanics eigenstates eigenvalues hermitian operators quantum measurements degeneracy expectation values time dependence

Quantum Ring Sequence

Students calculate the expectation value of energy and angular momentum as a function of time for an initial state for a particle on a ring. This state is a linear combination of energy/angular momentum eigenstates written in bra-ket notation.

group Small Group Activity

30 min.

Quantifying Change (Remote)

Thermo Derivatives

In this activity, students will explore how to calculate a derivative from measured data. Students should have prior exposure to differential calculus. At the start of the activity, orient the students to the contour plot - it's busy.

assignment Homework

Unknowns Spin-1/2 Brief
Quantum Fundamentals 2022 (2 years) With the Spins simulation set for a spin 1/2 system, measure the probabilities of all the possible spin components for each of the unknown initial states \(\left|{\psi_3}\right\rangle \) and \(\left|{\psi_4}\right\rangle \).
  1. Use your measured probabilities to find each of the unknown states as a linear superposition of the \(S_z\)-basis states \(\left|{+}\right\rangle \) and \(\left|{-}\right\rangle \).
  2. Articulate a Process: Write a set of general instructions that would allow another student in next year's class to find an unknown state from measured probabilities.
  3. Compare Theory with Experiment: Design an experiment that will allow you to test whether your prediction for each of the unknown states is correct. Describe your experiment here, clearly but succinctly, as if you were writing it up for a paper. Do the experiment and discuss your results.
  4. Make a Conceptual Connection: In general, can you determine a quantum state with spin-component probability measurements in only two spin-component-directions? Why or why not?

assignment Homework

Entropy of mixing
Entropy Equilibrium Sackur-Tetrode Thermal and Statistical Physics 2020

Suppose that a system of \(N\) atoms of type \(A\) is placed in diffusive contact with a system of \(N\) atoms of type \(B\) at the same temperature and volume.

  1. Show that after diffusive equilibrium is reached the total entropy is increased by \(2Nk\ln 2\). The entropy increase \(2Nk\ln 2\) is known as the entropy of mixing.

  2. If the atoms are identical (\(A=B\)), show that there is no increase in entropy when diffusive contact is established. The difference has been called the Gibbs paradox.

  3. Since the Helmholtz free energy is lower for the mixed \(AB\) than for the separated \(A\) and \(B\), it should be possible to extract work from the mixing process. Construct a process that could extract work as the two gasses are mixed at fixed temperature. You will probably need to use walls that are permeable to one gas but not the other.

Note

This course has not yet covered work, but it was covered in Energy and Entropy, so you may need to stretch your memory to finish part (c).

group Small Group Activity

10 min.

Using Tinker Toys to Represent Spin 1/2 Quantum Systems

spin 1/2 eigenstates quantum states

Arms Sequence for Complex Numbers and Quantum States

Students use Tinker Toys to represent each component in a two-state quantum spin system in all three standard bases (\(x\), \(y\), and \(z\)). Through a short series of instructor-led prompts, students explore the difference between overall phase (which does NOT change the state of the system) and relative phase (which does change the state of the system). This activity is optional in the Arms Sequence Arms Sequence for Complex Numbers and Quantum States.

assignment Homework

Isolength and Isoforce Stretchability
Energy and Entropy 2021 (2 years)

In class, you measured the isolength stretchability and the isoforce stretchability of your systems in the PDM. We found that for some systems these were very different, while for others they were identical.

Show with algebra (NOT experiment) that the ratio of isolength stretchability to isoforce stretchability is the same for both the left-hand side of the system and the right-hand side of the system. i.e.: \begin{align} \frac{\left(\frac{\partial {x_L}}{\partial {F_L}}\right)_{x_R}}{\left(\frac{\partial {x_L}}{\partial {F_L}}\right)_{F_R}} &= \frac{\left(\frac{\partial {x_R}}{\partial {F_R}}\right)_{x_L}}{\left(\frac{\partial {x_R}}{\partial {F_R}}\right)_{F_L}} \label{eq:ratios} \end{align}

Hint
You will need to make use of the cyclic chain rule: \begin{align} \left(\frac{\partial {A}}{\partial {B}}\right)_{C} = -\left(\frac{\partial {A}}{\partial {C}}\right)_{B}\left(\frac{\partial {C}}{\partial {B}}\right)_{A} \end{align}
Hint
You will also need the ordinary chain rule: \begin{align} \left(\frac{\partial {A}}{\partial {B}}\right)_{D} = \left(\frac{\partial {A}}{\partial {C}}\right)_{D}\left(\frac{\partial {C}}{\partial {B}}\right)_{D} \end{align}

biotech Experiment

60 min.

Microwave oven Ice Calorimetry Lab
Energy and Entropy 2021 (2 years)

heat entropy water ice thermodynamics

In this remote-friendly activity, students use a microwave oven (and optionally a thermometer) to measure the latent heat of melting for water (and optionally the heat capacity). From these they compute changes in entropy. See also Ice Calorimetry Lab.

assignment Homework

Spin Fermi Estimate
Quantum Fundamentals 2022 The following two problems ask you to make Fermi estimates. In a good Fermi estimate, you start from basic scientific facts you already know or quantities that you can reasonably estimate based on your life experiences and then reason your way to estimate a quantity that you would not be able guess. You may look up useful conversion factors or constants. Use words, pictures, and equations to explain your reasoning:
  1. Imagine that you send a pea-sized bead of silver through a Stern-Gerlach device oriented to measure the z-component of intrinsic spin. Estimate the total z-component of the intrinsic spin of the ball you would measure in the HIGHLY improbable case that every atom is spin up.
  2. Protons, neutrons, and electrons are all spin-1/2 particles. Give a (very crude) order of magnitude estimate of the number of these particles in your body.

keyboard Computational Activity

120 min.

Electrostatic potential of four point charges
Computational Physics Lab II 2022 (2 years)

electrostatic potential python

Students write python programs to compute and visualize the potential due to four point charges. For students with minimal programming ability and no python experience, this activity can be a good introduction to writing code in python using numpy and matplotlib.

group Small Group Activity

60 min.

Expectation Value and Uncertainty for the Difference of Dice
Quantum Fundamentals 2022 (2 years)

group Small Group Activity

30 min.

Superposition States for a Particle on a Ring

central forces quantum mechanics eigenstates eigenvalues quantum measurements angular momentum hermitian operators probability superposition

Quantum Ring Sequence

Students calculate probabilities for a particle on a ring whose wavefunction is not easily separated into eigenstates by inspection. To find the energy, angular momentum, and position probabilities, students perform integrations with the wavefunction or decompose the wavefunction into a superposition of eigenfunctions.

group Small Group Activity

60 min.

Establish Classroom Norms
Theoretical Mechanics 2021 (2 years)

Equity

In this hour-long activity, students establish classroom norms for being respectful when working in small groups. This is particularly helpful in the first course a cohort of students encounters.

group Small Group Activity

30 min.

Vector Surface and Volume Elements
Static Fields 2022 (3 years)

Integration Sequence

Students use known algebraic expressions for vector line elements \(d\vec{r}\) to determine all simple vector area \(d\vec{A}\) and volume elements \(d\tau\) in cylindrical and spherical coordinates.

This activity is identical to Scalar Surface and Volume Elements except uses a vector approach to find directed surface and volume elements.