## Activity: Sequential Stern-Gerlach Experiments

Quantum Fundamentals 2023 (3 years)
• Media
1. Set-Up a Sequential Measurement

1. Add an analyzer to the experiment by:

1. Break the links between the analyzer and the counters by clicking on the boxes with up and down arrow labels on the analyzer.
2. Click and drag a new connection from the analyzer to empty space to create a new element. A new analyzer is one of the options.

2. Measure $S_z$ twice in succession.

What is the probability that a particle leaving the first analyzer with $S_z=\frac{+\hbar}{2}$ will be measured by the second analyzer to have $S_z=\frac{-\hbar}{2}$?

3. Try all four possible combinations of input/outputs for the second analyzer.

What have you learned from these experiments?

2. Try All Combinations of Sequential Measurements

In the table, enter the probability of a particle exiting the 2nd analyzer with the spin indicated in row if the particle enters the 2nd analyzer with the spin indicated in each column.

3. You can rotate the Stern-Gerlach analyzers to any direction you want (using spherical coordinates).

Choose an arbitrary direction (not along one of the coordinate axes) for the 1st analyzer and measure the spin along the coordinate directions for the 2nd analyzer.

• face Statistical Analysis of Stern-Gerlach Experiments

face Lecture

30 min.

##### Statistical Analysis of Stern-Gerlach Experiments
• 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.
• group Mass is not Conserved

group Small Group Activity

30 min.

##### Mass is not Conserved
Theoretical Mechanics (4 years)

Groups are asked to analyze the following standard problem:

Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?

• face Introducing entropy

face Lecture

30 min.

##### Introducing entropy
Contemporary Challenges 2021 (4 years)

This lecture introduces the idea of entropy, including the relationship between entropy and multiplicity as well as the relationship between changes in entropy and heat.
• 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 Using $pV$ and $TS$ Plots

group Small Group Activity

30 min.

##### Using $pV$ and $TS$ Plots
Energy and Entropy 2021 (2 years)

Students work out heat and work for rectangular paths on $pV$ and $TS$ plots. This gives with computing heat and work, applying the First Law, and recognizing that internal energy is a state function, which cannot change after a cyclic process.
• group Quantum Expectation Values

group Small Group Activity

30 min.

##### Quantum Expectation Values
Quantum Fundamentals 2023 (3 years)
• assignment_ind Newton's 2nd Law SWBQ

assignment_ind Small White Board Question

5 min.

##### Newton's 2nd Law SWBQ
Central Forces 2023 (2 years)
• assignment Center of Mass for Two Uncoupled Particles

assignment Homework

##### Center of Mass for Two Uncoupled Particles
Central Forces 2023 (3 years)

(Straightforward) Purpose: Discover that a system of two masses can be a central force system even when they are not interacting at all. Practice with center-of-mass coordinates.

Consider two particles of equal mass $m$. The forces on the particles are $\vec F_1=0$ and $\vec F_2=F_0\hat{x}$. If the particles are initially at rest at the origin, find the position, velocity, and acceleration of the center of mass as functions of time. Solve this problem in two ways,

• with theorems about the center of mass motion,
• without theorems about the center of mass motion.
• Write a short description comparing the two solutions.

• accessibility_new Curvilinear Basis Vectors

accessibility_new Kinesthetic

10 min.

##### Curvilinear Basis Vectors
Static Fields 2023 (10 years)

Curvilinear Coordinate Sequence

Students use their arms to depict (sequentially) the different cylindrical and spherical basis vectors at the location of their shoulder (seen in relation to a specified origin of coordinates: either a set of axes hung from the ceiling of the room or perhaps a piece of furniture or a particular corner of the room).

Learning Outcomes