## Spin Three Halves Time Dependence

• 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 Lecture

5 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

face Lecture

5 min.

##### Unit Learning Outcomes: Quantum Mechanics on a Ring
Central Forces 2023
• group Generalized Leibniz Notation

group Small Group Activity

10 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 Activity

120 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 Question

30 min.

##### Magnetic Moment & Stern-Gerlach Experiments
Quantum Fundamentals 2023 (3 years)

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 Activity

60 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 Activity

30 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

group Small Group Activity

30 min.

##### Quantum Expectation Values
Quantum Fundamentals 2023 (3 years)
• 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, $\hat{H} = \alpha \hat{S}_x \doteq \frac{\alpha\hbar}{2}\begin{pmatrix} 0 & \sqrt{3} & 0 & 0\\ \sqrt{3} & 0 & 2 & 0\\ 0 & 2 & 0 & \sqrt{3} \\ 0 & 0 & \sqrt{3} & 0 \end{pmatrix}$
1. Find the energy eigenvalues and energy eigenstates for the system.
2. Find $|\psi(t)\rangle$.
3. List the outcomes of all possible measurements of $S_x$ and find their probabilities. Explicitly identify any probabilities that depend on time.
4. List the outcomes of all possible measurements of $S_z$ and find their probabilities. Explicitly identify any probabilities that depend on time.