📜 Module 3 · Lesson 2/3

🐱Superposition & Measurement

Being in several states at once — until someone looks. Hello, Schrödinger's cat!

⏱️ 16 minStart

🎯 By the end you will…

✓Define superposition
✓Predict measurement odds from α and β
✓Explain the point of Schrödinger's cat

Quantum waves can add together. If “spin up” is a valid state and “spin down” is a valid state, then a mix of both is valid too. This mix is called a superposition.

But when you measure, you never see a mix. You get one answer, at random, with odds set by the mix. After the measurement the system stays in the state you found — physicists say the wave function collapses.

🎛️Interactive experiment

This is a Bloch sphere: the North Pole is |0⟩, the South Pole is |1⟩, every other point is a superposition. Tilt the arrow, then press Measure many times and compare the counts with the predicted odds.

🧮Equation, decoded

A superposition of two states

∣ ψ ⟩ = α ∣0 ⟩ + β ∣1 ⟩, ∣ α ∣^{2} + ∣ β ∣^{2} = 1

What each symbol means

$∣0 ⟩, ∣1 ⟩$ Two basic states written in “ket” brackets, e.g. spin up / spin down
$α, β$ “alpha” and “beta”: how much of each state is in the mix (amplitudes)
$∣ α ∣^{2}$ The chance of measuring 0 (Born rule again!)
$= 1$ The chances must add up to 100%

📖 Say it like a story

It's a recipe: “take α parts of 0 and β parts of 1.” If α² = 0.7 and β² = 0.3, then measuring many identical copies gives 0 about 70% of the time and 1 about 30% of the time. Each single result is truly random.

✅ Check your understanding

Answer all questions to complete the lesson and earn XP.

1. What do you get when you measure a superposition?
2. If |α|² = 0.25, what is the chance of measuring 1?
3. Why did Schrödinger invent his cat story?

A superposition of two states

✅ Check your understanding

📚 Sources & further reading