One total chance and honest averages

Science · Quantum & Modern Physics · ages 19-20

Name ______________________ Date ____________

|Psi| squared is a probability density, not a probability.
Circle one: True False
What is the normalisation condition?
- Psi itself integrates to one
- Squared magnitude integrates to one
- Psi is zero everywhere
A ball is uniform in a tube. What is the chance it sits in the first half?
- 0.25
- 1
- 0.5
How is the expectation value of position computed?
- Integrate psi-star times x times psi
- Read the tallest peak of psi
- Average the wall positions
A tube is 4 m long with uniform normalised psi. Give the constant value of psi inside.
Answer: ______________
A state is symmetric about zero. What is its average position?
- Zero, since the sides balance
- The right wall
- Twice the peak position
Four trials give positions 1, 3, 3 and 5. Give the sample mean.
Answer: ______________
A student says the average position must be a spot where the particle can be found.
Circle one: True False

Answer key

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

True · You multiply by a width, or integrate, to get a chance.
Squared magnitude integrates to one · Total probability must be one, so |Psi| squared integrates to one.
0.5 · Half the length holds half the area under a flat density.
Integrate psi-star times x times psi · Each x is weighted by its density and summed.
0.5 · C squared times 4 is one, so C is 0.5.
Zero, since the sides balance · Left and right contributions cancel exactly.
3 · Add to 12 and divide by 4 to get 3.
False · An average over trials can land where no single trial lands.