*assignment*Spring Force Constant*assignment*Homework##### Spring Force Constant

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.*face*Unit Learning Outcomes: Classical Mechanics Orbits*face*Lecture5 min.

##### Unit Learning Outcomes: Classical Mechanics Orbits

Central Forces 2023 This handout lists Motivating Questions, Key Activities/Problems, Unit Learning Outcomes, and an Equation Sheet for a Unit on Classical Mechanics Orbits. It can be used both to introduce the unit and, even better, for review.*face*Unit Learning Outcomes: Quantum Mechanics on a Ring*group*Generalized Leibniz Notation*group*Small Group Activity10 min.

##### Generalized Leibniz Notation

Static Fields 2023 (6 years) This short small group activity introduces students to the Leibniz notation used for partial derivatives in thermodynamics; unlike standard Leibniz notation, this notation explicitly specifies constant variables. Students are guided in linking the variables from a contextless Leibniz-notation partial derivative to their proper variable categories.*group*Spin-1 Time Evolution*group*Small Group Activity120 min.

##### Spin-1 Time Evolution

Quantum Fundamentals 2023 Students do calculations for time evolution for spin-1.*assignment_ind*Magnetic Moment \& Stern-Gerlach Experiments*assignment_ind*Small White Board Question30 min.

##### Magnetic Moment & Stern-Gerlach Experiments

Quantum Fundamentals 2023 (3 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.*assignment*Curl*assignment*Homework##### Curl

Static Fields 2023 (6 years)Shown above is a two-dimensional cross-section of a vector field. All the parallel cross-sections of this field look exactly the same. Determine the direction of the curl at points A, B, and C.

*group*Establish Classroom Norms*group*Small Group Activity60 min.

##### Establish Classroom Norms

Theoretical Mechanics (4 years) 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*Quantum Measurement Play*group*Small Group Activity30 min.

##### Quantum Measurement Play

Quantum Fundamentals 2023 (2 years) The instructor and students do a skit where students represent quantum states that are “measured” by the instructor resulting in a state collapse.*group*Quantum Expectation Values-
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.