Level 2 · Secondary physics teaching kit · Grades 10–12
Quantum physics: states, amplitudes, and measurement
Use the learner record during the live investigation, then use the instructor guide to facilitate comparison, address misconceptions, and assess evidence-bounded reasoning.
Learner lab record
Wave-packet width and uncertainty record
How does narrowing a wave packet in position change its momentum spread and later evolution?
Setup
Use the wave-packet laboratory. Compare broad and narrow packets while keeping the central momentum fixed, then follow their modeled spreading over time.
Predict first
- 1. Predict which initial packet has the larger momentum spread.
- 2. Predict which packet spreads more rapidly in the free-particle model.
| Variable | Role | Unit |
|---|---|---|
| Initial position width | independent | model length |
| Central momentum | controlled | model momentum |
| Momentum spread | dependent | model momentum |
| Packet width over time | dependent | model length |
Observation columns
Analyze
- 1. Which comparison isolates initial width?
- 2. Does uncertainty describe instrument carelessness or the modeled state?
- 3. What does the probability distribution predict?
- 4. Which model assumptions limit the result?
Conclusion frame
Narrowing the initial packet from ___ to ___ changed momentum spread from ___ to ___ and later spreading by ___ because ___.
Instructor guide · 45–60 minutes
Teach the investigation, not the interface
Learning target: Learners connect localization with momentum spread without treating a wavefunction as a literal material wave or hidden classical path.
Prepare
- • Review probability distributions and standard deviation.
- • Distinguish central value from spread.
- • Prepare repeated-measurement language before opening the model.
Facilitation moves
- • Ask what an ensemble of trials would show.
- • Keep packet width separate from particle size.
- • Require learners to name the free-particle idealization.
Accessibility and participation
- • Pair every graph with a numeric center-and-spread table.
- • Describe widening verbally and avoid animation-only evidence.
- • Permit spreadsheet calculations for standard deviations.
Evidence of learning
- • A controlled width comparison
- • Correct center-versus-spread language
- • One stated model limitation
Misconception checks
Uncertainty is only poor measurement technique.
The modeled quantum state itself can have irreducible spreads even with ideal measurement.
The wave packet is a tiny classical cloud with a hidden exact trajectory.
It encodes amplitudes for possible outcomes; interpretations add different ontologies beyond the shared predictions.
Extension
Compare free spreading with a confined packet and identify which Hamiltonian term changes the evolution.