Adding two spins into a total

Science · Quantum & Modern Physics · ages 23-24

Name ______________________ Date ____________

Each spin-half carries two states. How many states in the product picture?
- 3
- 2
- 4
Two momenta combine. Which totals are allowed?
- Only the sum itself
- From the difference to the sum
- Only the difference itself
The coupled basis adds brand-new states beyond the product ones.
Circle one: True False
Your coupled count is 4 but a friend's product count is 6. What do you conclude?
- Someone miscounted, since the totals must agree
- Both counts can be right at once
- Bases always disagree
Total one carries three states and total zero carries one. How many coupled states is that in total?
Answer: ______________
How is one coupled state of two spins written?
- As a single product state always
- As a combination of product states
- Without using product states
A spectrum shows a level split into groups of three states plus one state. What does the lesson suggest?
- Two spin-half pieces combining into totals one and zero
- Three unrelated particles colliding
- A single spin with no partner
Two spin-half particles: a friend claims totals zero, one, and two all appear. What is wrong?
- Zero can never appear
- Only total two can appear
- Two is above the sum, so it cannot appear

Answer key

For grown-ups. Fold this page away before handing over the rest.

4 · Multiply the two counts: two times two.
From the difference to the sum · Allowed totals run difference through sum.
False · It relabels the same states; the count never changes.
Someone miscounted, since the totals must agree · Two bases, one state space: counts must match.
4 · Add what each total carries: three plus one is four.
As a combination of product states · Coupled states mix product states together.
Two spin-half pieces combining into totals one and zero · Three plus one is the two-spin-half fingerprint.
Two is above the sum, so it cannot appear · The sum caps the totals at one here.